Greek Letters Used In Mathematics, Science, And Engineering
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mathematics Mathematics is a field of study that discovers and organizes methods, Mathematical theory, theories and theorems that are developed and Mathematical proof, proved for the needs of empirical sciences and mathematics itself. There are many ar ...
,
science Science is a systematic discipline that builds and organises knowledge in the form of testable hypotheses and predictions about the universe. Modern science is typically divided into twoor threemajor branches: the natural sciences, which stu ...
,
engineering Engineering is the practice of using natural science, mathematics, and the engineering design process to Problem solving#Engineering, solve problems within technology, increase efficiency and productivity, and improve Systems engineering, s ...
, and other areas where mathematical notation is used as symbols for constants,
special function Special functions are particular mathematical functions that have more or less established names and notations due to their importance in mathematical analysis, functional analysis, geometry, physics, or other applications. The term is defined by ...
s, and also conventionally for variables representing certain quantities. In these contexts, the capital letters and the small letters represent distinct and unrelated entities. Those Greek letters which have the same form as Latin letters are rarely used: capital Α, Β, Ε, Ζ, Η, Ι, Κ, Μ, Ν, Ο, Ρ, Τ, Υ, and Χ. Small ι, ο and υ are also rarely used, since they closely resemble the Latin letters i, o and u. Sometimes, font variants of Greek letters are used as distinct symbols in mathematics, in particular for ε/ϵ and π/ϖ. The archaic letter
digamma Digamma or wau (uppercase: Ϝ, lowercase: ϝ, numeral: ϛ) is an Archaic Greek alphabets, archaic letter of the Greek alphabet. It originally stood for the sound but it has remained in use principally as a Greek numeral for 6 (number), 6. Whe ...
(Ϝ/ϝ/ϛ) is sometimes used. The
Bayer designation A Bayer designation is a stellar designation in which a specific star is identified by a Greek alphabet, Greek or Latin letter followed by the genitive case, genitive form of its parent constellation's Latin name. The original list of Bayer design ...
naming scheme for
star A star is a luminous spheroid of plasma (physics), plasma held together by Self-gravitation, self-gravity. The List of nearest stars and brown dwarfs, nearest star to Earth is the Sun. Many other stars are visible to the naked eye at night sk ...
s typically uses the first Greek letter, α, for the brightest star in each constellation, and runs through the alphabet before switching to Latin letters. In
mathematical finance Mathematical finance, also known as quantitative finance and financial mathematics, is a field of applied mathematics, concerned with mathematical modeling in the financial field. In general, there exist two separate branches of finance that req ...
, the Greeks are the variables denoted by Greek letters used to describe the risk of certain investments.


Typography

Some common conventions: * Intensive quantities in
physics Physics is the scientific study of matter, its Elementary particle, fundamental constituents, its motion and behavior through space and time, and the related entities of energy and force. "Physical science is that department of knowledge whi ...
are usually denoted with minuscules
while extensive are denoted with
capital letter Letter case is the distinction between the letters that are in larger uppercase or capitals (more formally ''majuscule'') and smaller lowercase (more formally '' minuscule'') in the written representation of certain languages. The writing system ...
s. * Most symbols are written in italics. * Vectors can be denoted in boldface. * Sets of
number A number is a mathematical object used to count, measure, and label. The most basic examples are the natural numbers 1, 2, 3, 4, and so forth. Numbers can be represented in language with number words. More universally, individual numbers can ...
s are typically bold or blackboard bold. The Greek letter forms used in mathematics are often different from those used in Greek-language text: they are designed to be used in isolation, not connected to other letters, and some use variant forms which are not normally used in current Greek typography. The OpenType font format has the feature tag "mgrk" ("Mathematical Greek") to identify a
glyph A glyph ( ) is any kind of purposeful mark. In typography, a glyph is "the specific shape, design, or representation of a character". It is a particular graphical representation, in a particular typeface, of an element of written language. A ...
as representing a Greek letter to be used in mathematical (as opposed to Greek language) contexts. The table below shows a comparison of Greek letters rendered in
TeX Tex, TeX, TEX, may refer to: People and fictional characters * Tex (nickname), a list of people and fictional characters with the nickname * Tex Earnhardt (1930–2020), U.S. businessman * Joe Tex (1933–1982), stage name of American soul singer ...
and HTML. The font used in the TeX rendering is an italic style. This is in line with the convention that variables should be italicized. As Greek letters are more often than not used as variables in mathematical formulas, a Greek letter appearing similar to the TeX rendering is more likely to be encountered in works involving mathematics.


Concepts represented by a Greek letter


Αα (alpha)

* \alpha represents: ** the first
angle In Euclidean geometry, an angle can refer to a number of concepts relating to the intersection of two straight Line (geometry), lines at a Point (geometry), point. Formally, an angle is a figure lying in a Euclidean plane, plane formed by two R ...
in a
triangle A triangle is a polygon with three corners and three sides, one of the basic shapes in geometry. The corners, also called ''vertices'', are zero-dimensional points while the sides connecting them, also called ''edges'', are one-dimension ...
, opposite the side ''a'' ** the
statistical significance In statistical hypothesis testing, a result has statistical significance when a result at least as "extreme" would be very infrequent if the null hypothesis were true. More precisely, a study's defined significance level, denoted by \alpha, is the ...
of a result ** the false positive rate in statistics ("Type I" error) ** the
fine-structure constant In physics, the fine-structure constant, also known as the Sommerfeld constant, commonly denoted by (the Alpha, Greek letter ''alpha''), is a Dimensionless physical constant, fundamental physical constant that quantifies the strength of the el ...
in physics ** the angle of attack of an aircraft ** an
alpha particle Alpha particles, also called alpha rays or alpha radiation, consist of two protons and two neutrons bound together into a particle identical to a helium-4 nucleus. They are generally produced in the process of alpha decay but may also be produce ...
(He2+) ** angular acceleration in physics ** the linear thermal expansion coefficient ** the
thermal diffusivity In thermodynamics, thermal diffusivity is the thermal conductivity divided by density and specific heat capacity at constant pressure. It is a measure of the rate of heat transfer inside a material and has SI, SI units of m2/s. It is an intensive ...
** In
organic chemistry Organic chemistry is a subdiscipline within chemistry involving the science, scientific study of the structure, properties, and reactions of organic compounds and organic matter, organic materials, i.e., matter in its various forms that contain ...
the α-carbon is the backbone carbon next to the carbonyl carbon, most often for
amino acids Amino acids are organic compounds that contain both amino and carboxylic acid functional groups. Although over 500 amino acids exist in nature, by far the most important are the Proteinogenic amino acid, 22 α-amino acids incorporated into p ...
**
right ascension Right ascension (abbreviated RA; symbol ) is the angular distance of a particular point measured eastward along the celestial equator from the Sun at the equinox (celestial coordinates), March equinox to the (hour circle of the) point in questio ...
in
astronomy Astronomy is a natural science that studies celestial objects and the phenomena that occur in the cosmos. It uses mathematics, physics, and chemistry in order to explain their origin and their overall evolution. Objects of interest includ ...
** the brightest star in a constellation ** Iron ferrite and numerous phases within materials science ** the return in excess of the compensation for the risk borne in investment ** the
α-conversion In mathematical logic, the lambda calculus (also written as ''λ''-calculus) is a formal system for expressing computation based on function abstraction and application using variable binding and substitution. Untyped lambda calculus, the topic ...
in
lambda calculus In mathematical logic, the lambda calculus (also written as ''λ''-calculus) is a formal system for expressing computability, computation based on function Abstraction (computer science), abstraction and function application, application using var ...
** the independence number of a graph ** a placeholder for
ordinal numbers In set theory, an ordinal number, or ordinal, is a generalization of ordinal numerals (first, second, th, etc.) aimed to extend enumeration to infinite sets. A finite set can be enumerated by successively labeling each element with the leas ...
in
mathematical logic Mathematical logic is the study of Logic#Formal logic, formal logic within mathematics. Major subareas include model theory, proof theory, set theory, and recursion theory (also known as computability theory). Research in mathematical logic com ...
** a type of receptor for the neurotransmitter noradrenaline in
neuroscience Neuroscience is the scientific study of the nervous system (the brain, spinal cord, and peripheral nervous system), its functions, and its disorders. It is a multidisciplinary science that combines physiology, anatomy, molecular biology, ...


Ββ (beta)

* \Beta represents the beta function * \beta represents: ** the thermodynamic beta, equal to (''k''B''T'')−1, where ''k''B is the Boltzmann constant and ''T'' is the absolute temperature. ** the second angle in a
triangle A triangle is a polygon with three corners and three sides, one of the basic shapes in geometry. The corners, also called ''vertices'', are zero-dimensional points while the sides connecting them, also called ''edges'', are one-dimension ...
, opposite the side ''b'' ** the standardized regression coefficient for predictor or independent variables in
linear regression In statistics, linear regression is a statistical model, model that estimates the relationship between a Scalar (mathematics), scalar response (dependent variable) and one or more explanatory variables (regressor or independent variable). A mode ...
(unstandardized regression coefficients are represented with the lower-case Latin b, but are often called "betas" as well) ** the ratio of collector current to base current in a bipolar junction
transistor A transistor is a semiconductor device used to Electronic amplifier, amplify or electronic switch, switch electrical signals and electric power, power. It is one of the basic building blocks of modern electronics. It is composed of semicondu ...
(BJT) in electronics (current gain) ** the false negative rate in statistics ("Type II" error) ** the beta coefficient, the non-diversifiable risk, of an asset in
mathematical finance Mathematical finance, also known as quantitative finance and financial mathematics, is a field of applied mathematics, concerned with mathematical modeling in the financial field. In general, there exist two separate branches of finance that req ...
** the sideslip angle of an airplane ** a beta particle (e or e+) ** the beta brain wave in
brain The brain is an organ (biology), organ that serves as the center of the nervous system in all vertebrate and most invertebrate animals. It consists of nervous tissue and is typically located in the head (cephalization), usually near organs for ...
or
cognitive sciences Cognitive science is the interdisciplinary, scientific study of the mind and its processes. It examines the nature, the tasks, and the functions of cognition (in a broad sense). Mental faculties of concern to cognitive scientists include percep ...
** ecliptic latitude in
astronomy Astronomy is a natural science that studies celestial objects and the phenomena that occur in the cosmos. It uses mathematics, physics, and chemistry in order to explain their origin and their overall evolution. Objects of interest includ ...
** the ratio of plasma pressure to magnetic pressure in plasma physics **
β-reduction In mathematical logic, the lambda calculus (also written as ''λ''-calculus) is a formal system for expressing computation based on function abstraction and application using variable binding and substitution. Untyped lambda calculus, the topic ...
in
lambda calculus In mathematical logic, the lambda calculus (also written as ''λ''-calculus) is a formal system for expressing computability, computation based on function Abstraction (computer science), abstraction and function application, application using var ...
** the ratio of the velocity of an object to the
speed of light The speed of light in vacuum, commonly denoted , is a universal physical constant exactly equal to ). It is exact because, by international agreement, a metre is defined as the length of the path travelled by light in vacuum during a time i ...
as used in the
Lorentz factor The Lorentz factor or Lorentz term (also known as the gamma factor) is a dimensionless quantity expressing how much the measurements of time, length, and other physical properties change for an object while it moves. The expression appears in sev ...
** a type of receptor for the noradrenaline neurotransmitter in
neuroscience Neuroscience is the scientific study of the nervous system (the brain, spinal cord, and peripheral nervous system), its functions, and its disorders. It is a multidisciplinary science that combines physiology, anatomy, molecular biology, ...


Γγ (gamma)

* \Gamma represents: ** the circulation in
fluid dynamics In physics, physical chemistry and engineering, fluid dynamics is a subdiscipline of fluid mechanics that describes the flow of fluids – liquids and gases. It has several subdisciplines, including (the study of air and other gases in motion ...
** the reflection coefficient of a transmission or telecommunication line. ** the confinement factor of an optical mode in a waveguide ** the
gamma function In mathematics, the gamma function (represented by Γ, capital Greek alphabet, Greek letter gamma) is the most common extension of the factorial function to complex numbers. Derived by Daniel Bernoulli, the gamma function \Gamma(z) is defined ...
, a generalization of the
factorial In mathematics, the factorial of a non-negative denoted is the Product (mathematics), product of all positive integers less than or equal The factorial also equals the product of n with the next smaller factorial: \begin n! &= n \times ...
** the
upper incomplete gamma function In mathematics, the upper and lower incomplete gamma functions are types of special functions which arise as solutions to various mathematical problems such as certain integrals. Their respective names stem from their integral definitions, whic ...
** the modular group, the group of fractional linear transformations ** the gamma distribution, a continuous probability distribution defined using the
gamma function In mathematics, the gamma function (represented by Γ, capital Greek alphabet, Greek letter gamma) is the most common extension of the factorial function to complex numbers. Derived by Daniel Bernoulli, the gamma function \Gamma(z) is defined ...
** second-order sensitivity to price in
mathematical finance Mathematical finance, also known as quantitative finance and financial mathematics, is a field of applied mathematics, concerned with mathematical modeling in the financial field. In general, there exist two separate branches of finance that req ...
** the Christoffel symbols that describe components of a metric connection ** the stack alphabet in the formal definition of a pushdown automaton, or the tape-alphabet in the formal definition of a
Turing machine A Turing machine is a mathematical model of computation describing an abstract machine that manipulates symbols on a strip of tape according to a table of rules. Despite the model's simplicity, it is capable of implementing any computer algori ...
** the Feferman–Schütte ordinal Γ0 ** atmospheric lapse rates in
meteorology Meteorology is the scientific study of the Earth's atmosphere and short-term atmospheric phenomena (i.e. weather), with a focus on weather forecasting. It has applications in the military, aviation, energy production, transport, agricultur ...
* \gamma represents: ** the specific weight of substances ** the lower incomplete gamma function ** the third angle in a
triangle A triangle is a polygon with three corners and three sides, one of the basic shapes in geometry. The corners, also called ''vertices'', are zero-dimensional points while the sides connecting them, also called ''edges'', are one-dimension ...
, opposite the side ''c'' ** the Euler–Mascheroni constant in mathematics **
gamma ray A gamma ray, also known as gamma radiation (symbol ), is a penetrating form of electromagnetic radiation arising from high energy interactions like the radioactive decay of atomic nuclei or astronomical events like solar flares. It consists o ...
s and the
photon A photon () is an elementary particle that is a quantum of the electromagnetic field, including electromagnetic radiation such as light and radio waves, and the force carrier for the electromagnetic force. Photons are massless particles that can ...
** the heat capacity ratio in
thermodynamics Thermodynamics is a branch of physics that deals with heat, Work (thermodynamics), work, and temperature, and their relation to energy, entropy, and the physical properties of matter and radiation. The behavior of these quantities is governed b ...
** the
Lorentz factor The Lorentz factor or Lorentz term (also known as the gamma factor) is a dimensionless quantity expressing how much the measurements of time, length, and other physical properties change for an object while it moves. The expression appears in sev ...
in special relativity ** the flight path angle of an airplane


Δδ (delta)

* \Delta represents: ** a
finite difference A finite difference is a mathematical expression of the form . Finite differences (or the associated difference quotients) are often used as approximations of derivatives, such as in numerical differentiation. The difference operator, commonly d ...
** a difference operator ** a
symmetric difference In mathematics, the symmetric difference of two sets, also known as the disjunctive union and set sum, is the set of elements which are in either of the sets, but not in their intersection. For example, the symmetric difference of the sets \ and ...
** the
Laplace operator In mathematics, the Laplace operator or Laplacian is a differential operator given by the divergence of the gradient of a Scalar field, scalar function on Euclidean space. It is usually denoted by the symbols \nabla\cdot\nabla, \nabla^2 (where \ ...
** giving heat in a
chemical reaction A chemical reaction is a process that leads to the chemistry, chemical transformation of one set of chemical substances to another. When chemical reactions occur, the atoms are rearranged and the reaction is accompanied by an Gibbs free energy, ...
** the angle that subtends the arc of a circular curve in
surveying Surveying or land surveying is the technique, profession, art, and science of determining the land, terrestrial Plane (mathematics), two-dimensional or Three-dimensional space#In Euclidean geometry, three-dimensional positions of Point (geom ...
** the maximum degree of any vertex in a given graph ** sensitivity to price in
mathematical finance Mathematical finance, also known as quantitative finance and financial mathematics, is a field of applied mathematics, concerned with mathematical modeling in the financial field. In general, there exist two separate branches of finance that req ...
** the discriminant of a polynomial (in a quadratic polynomial determines the nature of the roots) * \delta represents: ** percent error ** a variation in the
calculus of variations The calculus of variations (or variational calculus) is a field of mathematical analysis that uses variations, which are small changes in Function (mathematics), functions and functional (mathematics), functionals, to find maxima and minima of f ...
** the
Kronecker delta In mathematics, the Kronecker delta (named after Leopold Kronecker) is a function of two variables, usually just non-negative integers. The function is 1 if the variables are equal, and 0 otherwise: \delta_ = \begin 0 &\text i \neq j, \\ 1 &\ ...
function ** the Feigenbaum constants ** the force of interest in
mathematical finance Mathematical finance, also known as quantitative finance and financial mathematics, is a field of applied mathematics, concerned with mathematical modeling in the financial field. In general, there exist two separate branches of finance that req ...
** the
Dirac delta function In mathematical analysis, the Dirac delta function (or distribution), also known as the unit impulse, is a generalized function on the real numbers, whose value is zero everywhere except at zero, and whose integral over the entire real line ...
** the receptor which enkephalins have the highest affinity for in
pharmacology Pharmacology is the science of drugs and medications, including a substance's origin, composition, pharmacokinetics, pharmacodynamics, therapeutic use, and toxicology. More specifically, it is the study of the interactions that occur betwee ...
Katzung & Trevor's Pharmacology Examination & Board Review (9th Edition.). Anthony J. Trevor, Bertram G. Katzung, Susan B. Masters . B. Opioid Peptides + 268 pp. ** the Skorokhod integral in Malliavin calculus, a subfield of stochastic analysis ** the minimum degree of any vertex in a given graph ** a partial charge. δ− represents a negative partial charge, and δ+ represents a positive partial charge
chemistry Chemistry is the scientific study of the properties and behavior of matter. It is a physical science within the natural sciences that studies the chemical elements that make up matter and chemical compound, compounds made of atoms, molecules a ...
(See also: Solvation) ** the chemical shift of an atomic nucleus in NMR spectroscopy. For protons, this is relative to tetramethylsilane = 0 ** stable isotope compositions **
declination In astronomy, declination (abbreviated dec; symbol ''δ'') is one of the two angles that locate a point on the celestial sphere in the equatorial coordinate system, the other being hour angle. The declination angle is measured north (positive) or ...
in
astronomy Astronomy is a natural science that studies celestial objects and the phenomena that occur in the cosmos. It uses mathematics, physics, and chemistry in order to explain their origin and their overall evolution. Objects of interest includ ...
** noncentrality measure in
statistics Statistics (from German language, German: ', "description of a State (polity), state, a country") is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data. In applying statistics to a s ...
** The transition function in the formal definition of a finite automaton, pushdown automaton, or
Turing machine A Turing machine is a mathematical model of computation describing an abstract machine that manipulates symbols on a strip of tape according to a table of rules. Despite the model's simplicity, it is capable of implementing any computer algori ...
**
Infinitesimal In mathematics, an infinitesimal number is a non-zero quantity that is closer to 0 than any non-zero real number is. The word ''infinitesimal'' comes from a 17th-century Modern Latin coinage ''infinitesimus'', which originally referred to the " ...
- see * Not to be confused with which is based on the Latin letter d but often called a "script delta"


Εε (epsilon)

* \epsilon represents: ** a small positive quantity; see limit ** a random error in regression analysis ** the absolute value of an error ** in
set theory Set theory is the branch of mathematical logic that studies Set (mathematics), sets, which can be informally described as collections of objects. Although objects of any kind can be collected into a set, set theory – as a branch of mathema ...
, the limit ordinal of the sequence \omega,\omega^,\omega^,\dots ** in
computer science Computer science is the study of computation, information, and automation. Computer science spans Theoretical computer science, theoretical disciplines (such as algorithms, theory of computation, and information theory) to Applied science, ...
, the
empty string In formal language theory, the empty string, or empty word, is the unique String (computer science), string of length zero. Formal theory Formally, a string is a finite, ordered sequence of character (symbol), characters such as letters, digits ...
** the Levi-Civita symbol ** in electromagnetics,
dielectric In electromagnetism, a dielectric (or dielectric medium) is an Insulator (electricity), electrical insulator that can be Polarisability, polarised by an applied electric field. When a dielectric material is placed in an electric field, electric ...
permittivity In electromagnetism, the absolute permittivity, often simply called permittivity and denoted by the Greek letter (epsilon), is a measure of the electric polarizability of a dielectric material. A material with high permittivity polarizes more ...
** emissivity ** strain in
continuum mechanics Continuum mechanics is a branch of mechanics that deals with the deformation of and transmission of forces through materials modeled as a ''continuous medium'' (also called a ''continuum'') rather than as discrete particles. Continuum mec ...
**
permittivity In electromagnetism, the absolute permittivity, often simply called permittivity and denoted by the Greek letter (epsilon), is a measure of the electric polarizability of a dielectric material. A material with high permittivity polarizes more ...
** the Earth's
axial tilt In astronomy, axial tilt, also known as obliquity, is the angle between an object's rotational axis and its orbital axis, which is the line perpendicular to its orbital plane; equivalently, it is the angle between its equatorial plane and orbita ...
in
astronomy Astronomy is a natural science that studies celestial objects and the phenomena that occur in the cosmos. It uses mathematics, physics, and chemistry in order to explain their origin and their overall evolution. Objects of interest includ ...
** elasticity in
economics Economics () is a behavioral science that studies the Production (economics), production, distribution (economics), distribution, and Consumption (economics), consumption of goods and services. Economics focuses on the behaviour and interac ...
**
electromotive force In electromagnetism and electronics, electromotive force (also electromotance, abbreviated emf, denoted \mathcal) is an energy transfer to an electric circuit per unit of electric charge, measured in volts. Devices called electrical ''transducer ...
** in
chemistry Chemistry is the scientific study of the properties and behavior of matter. It is a physical science within the natural sciences that studies the chemical elements that make up matter and chemical compound, compounds made of atoms, molecules a ...
, the molar extinction coefficient of a
chromophore A chromophore is the part of a molecule responsible for its color. The word is derived . The color that is seen by our eyes is that of the light not Absorption (electromagnetic radiation), absorbed by the reflecting object within a certain wavele ...
** in mathematics, a surreal number that is bigger than zero, but smaller than all positive real numbers. *
set Set, The Set, SET or SETS may refer to: Science, technology, and mathematics Mathematics *Set (mathematics), a collection of elements *Category of sets, the category whose objects and morphisms are sets and total functions, respectively Electro ...
membership symbol ∈ is based on ε


(digamma)

* is sometimes used to represent the digamma function, though the Latin letter F (which is nearly identical) is usually substituted. * A hypothetical particle Ϝ speculated to be implicated in the 750 GeV diphoton excess, now known to be simply a statistical anomaly


Ζζ (zeta)

* \zeta represents: ** the Riemann zeta function and other zeta functions in mathematics ** the damping ratio ** the value for the Zeta potential, i.e., the electrical potential at the slipping plane, used often in colloidal chemistry


Ηη (eta)

* \Eta represents: ** the Eta function of
Ludwig Boltzmann Ludwig Eduard Boltzmann ( ; ; 20 February 1844 – 5 September 1906) was an Austrian mathematician and Theoretical physics, theoretical physicist. His greatest achievements were the development of statistical mechanics and the statistical ex ...
's H-theorem ("Eta" theorem), in
statistical mechanics In physics, statistical mechanics is a mathematical framework that applies statistical methods and probability theory to large assemblies of microscopic entities. Sometimes called statistical physics or statistical thermodynamics, its applicati ...
** Information theoretic (Shannon) entropy * \eta represents: ** the intrinsic wave impedance of a medium (e.g. the impedance of free space) ** the partial regression
coefficient In mathematics, a coefficient is a Factor (arithmetic), multiplicative factor involved in some Summand, term of a polynomial, a series (mathematics), series, or any other type of expression (mathematics), expression. It may be a Dimensionless qu ...
in statistics, also interpreted as an effect size measure for analyses of variance ** the eta meson **
viscosity Viscosity is a measure of a fluid's rate-dependent drag (physics), resistance to a change in shape or to movement of its neighboring portions relative to one another. For liquids, it corresponds to the informal concept of ''thickness''; for e ...
** the Dedekind eta function ** energy conversion efficiency ** efficiency (physics) ** the
Minkowski metric In physics, Minkowski space (or Minkowski spacetime) () is the main mathematical description of spacetime in the absence of general_relativity, gravitation. It combines inertial space and time manifolds into a four-dimensional model. The model ...
tensor in relativity ** η-conversion in
lambda calculus In mathematical logic, the lambda calculus (also written as ''λ''-calculus) is a formal system for expressing computability, computation based on function Abstraction (computer science), abstraction and function application, application using var ...
** the learning rate in machine learning and statistics


Θθ (theta)

* \Theta (uppercase) represents: ** an asymptotically tight bound related to
big O notation Big ''O'' notation is a mathematical notation that describes the asymptotic analysis, limiting behavior of a function (mathematics), function when the Argument of a function, argument tends towards a particular value or infinity. Big O is a memb ...
. ** sensitivity to the passage of time in
mathematical finance Mathematical finance, also known as quantitative finance and financial mathematics, is a field of applied mathematics, concerned with mathematical modeling in the financial field. In general, there exist two separate branches of finance that req ...
** in
set theory Set theory is the branch of mathematical logic that studies Set (mathematics), sets, which can be informally described as collections of objects. Although objects of any kind can be collected into a set, set theory – as a branch of mathema ...
, a certain ordinal number ** Heaviside step function * \theta (lowercase) represents: ** a plane angle in
geometry Geometry (; ) is a branch of mathematics concerned with properties of space such as the distance, shape, size, and relative position of figures. Geometry is, along with arithmetic, one of the oldest branches of mathematics. A mathematician w ...
** the
angle In Euclidean geometry, an angle can refer to a number of concepts relating to the intersection of two straight Line (geometry), lines at a Point (geometry), point. Formally, an angle is a figure lying in a Euclidean plane, plane formed by two R ...
to the ''x'' axis in the ''xy''- plane in spherical or cylindrical coordinates (mathematics) ** the
angle In Euclidean geometry, an angle can refer to a number of concepts relating to the intersection of two straight Line (geometry), lines at a Point (geometry), point. Formally, an angle is a figure lying in a Euclidean plane, plane formed by two R ...
to the ''z'' axis in spherical coordinates (physics) ** the potential temperature in thermodynamics ** theta functions ** the angle of a scattered photon during a Compton scattering interaction ** the angular displacement of a particle rotating about an axis ** the Watterson estimator in population genetics ** the thermal resistance between two bodies * ("script theta"), the cursive form of theta, often used in handwriting, represents ** the first Chebyshev function in
number theory Number theory is a branch of pure mathematics devoted primarily to the study of the integers and arithmetic functions. Number theorists study prime numbers as well as the properties of mathematical objects constructed from integers (for example ...
** Theta role in linguistics


Ιι (iota)

* \iota represents: ** an inclusion map in
set theory Set theory is the branch of mathematical logic that studies Set (mathematics), sets, which can be informally described as collections of objects. Although objects of any kind can be collected into a set, set theory – as a branch of mathema ...
** the index generator function in APL (in the form ⍳) ** the
interior product In mathematics, the interior product (also known as interior derivative, interior multiplication, inner multiplication, inner derivative, insertion operator, contraction, or inner derivation) is a degree −1 (anti)derivation on the exterio ...


Κκ (kappa)

* \Kappa represents: ** the Kappa number, indicating lignin content in pulp * \kappa represents: ** the Von Kármán constant, describing the velocity profile of turbulent flow ** the kappa curve, a two-dimensional algebraic curve ** the condition number of a matrix in
numerical analysis Numerical analysis is the study of algorithms that use numerical approximation (as opposed to symbolic computation, symbolic manipulations) for the problems of mathematical analysis (as distinguished from discrete mathematics). It is the study of ...
** the connectivity of a graph in
graph theory In mathematics and computer science, graph theory is the study of ''graph (discrete mathematics), graphs'', which are mathematical structures used to model pairwise relations between objects. A graph in this context is made up of ''Vertex (graph ...
**
curvature In mathematics, curvature is any of several strongly related concepts in geometry that intuitively measure the amount by which a curve deviates from being a straight line or by which a surface deviates from being a plane. If a curve or su ...
**
dielectric constant The relative permittivity (in older texts, dielectric constant) is the permittivity of a material expressed as a ratio with the electric permittivity of a vacuum. A dielectric is an insulating material, and the dielectric constant of an insul ...
(\varepsilon / \varepsilon_0) **
thermal conductivity The thermal conductivity of a material is a measure of its ability to heat conduction, conduct heat. It is commonly denoted by k, \lambda, or \kappa and is measured in W·m−1·K−1. Heat transfer occurs at a lower rate in materials of low ...
(usually a lowercase Latin k) **
electrical conductivity Electrical resistivity (also called volume resistivity or specific electrical resistance) is a fundamental specific property of a material that measures its electrical resistance or how strongly it resists electric current. A low resistivity in ...
of a solution **
thermal diffusivity In thermodynamics, thermal diffusivity is the thermal conductivity divided by density and specific heat capacity at constant pressure. It is a measure of the rate of heat transfer inside a material and has SI, SI units of m2/s. It is an intensive ...
** a
spring constant In physics, Hooke's law is an empirical law which states that the force () needed to extend or compress a spring (device), spring by some distance () Proportionality (mathematics)#Direct_proportionality, scales linearly with respect to that ...
(usually a lowercase Latin k) ** the heat capacity ratio in thermodynamics (usually \gamma) ** the receptor which dynorphins have the highest affinity for in
pharmacology Pharmacology is the science of drugs and medications, including a substance's origin, composition, pharmacokinetics, pharmacodynamics, therapeutic use, and toxicology. More specifically, it is the study of the interactions that occur betwee ...
** Einstein gravitational constant


Λλ (lambda)

* \Lambda represents: ** the Lebesgue constant, a bound for the interpolation error ** the
von Mangoldt function In mathematics, the von Mangoldt function is an arithmetic function named after German mathematician Hans von Mangoldt. It is an example of an important arithmetic function that is neither multiplicative nor additive. Definition The von Mang ...
in
number theory Number theory is a branch of pure mathematics devoted primarily to the study of the integers and arithmetic functions. Number theorists study prime numbers as well as the properties of mathematical objects constructed from integers (for example ...
** the set of logical axioms in the
axiomatic method In mathematics and logic, an axiomatic system is a set of formal statements (i.e. axioms) used to logically derive other statements such as lemmas or theorems. A proof within an axiom system is a sequence of deductive steps that establis ...
of logical deduction in first-order logic ** the cosmological constant ** the lambda baryon ** a diagonal matrix of
eigenvalue In linear algebra, an eigenvector ( ) or characteristic vector is a vector that has its direction unchanged (or reversed) by a given linear transformation. More precisely, an eigenvector \mathbf v of a linear transformation T is scaled by a ...
s in
linear algebra Linear algebra is the branch of mathematics concerning linear equations such as :a_1x_1+\cdots +a_nx_n=b, linear maps such as :(x_1, \ldots, x_n) \mapsto a_1x_1+\cdots +a_nx_n, and their representations in vector spaces and through matrix (mathemat ...
** a lattice ** molar conductivity in electrochemistry ** Iwasawa algebra * \lambda represents: ** one
wavelength In physics and mathematics, wavelength or spatial period of a wave or periodic function is the distance over which the wave's shape repeats. In other words, it is the distance between consecutive corresponding points of the same ''phase (waves ...
of electromagnetic radiation ** the decay constant in radioactivity ** function expressions in the
lambda calculus In mathematical logic, the lambda calculus (also written as ''λ''-calculus) is a formal system for expressing computability, computation based on function Abstraction (computer science), abstraction and function application, application using var ...
** a general
eigenvalue In linear algebra, an eigenvector ( ) or characteristic vector is a vector that has its direction unchanged (or reversed) by a given linear transformation. More precisely, an eigenvector \mathbf v of a linear transformation T is scaled by a ...
in
linear algebra Linear algebra is the branch of mathematics concerning linear equations such as :a_1x_1+\cdots +a_nx_n=b, linear maps such as :(x_1, \ldots, x_n) \mapsto a_1x_1+\cdots +a_nx_n, and their representations in vector spaces and through matrix (mathemat ...
** the expected number of occurrences in a Poisson distribution in probability ** the arrival rate in
queueing theory Queueing theory is the mathematical study of waiting lines, or queues. A queueing model is constructed so that queue lengths and waiting time can be predicted. Queueing theory is generally considered a branch of operations research because th ...
** the
failure rate Failure is the social concept of not meeting a desirable or intended objective, and is usually viewed as the opposite of success. The criteria for failure depends on context, and may be relative to a particular observer or belief system. On ...
in
reliability engineering Reliability engineering is a sub-discipline of systems engineering that emphasizes the ability of equipment to function without failure. Reliability is defined as the probability that a product, system, or service will perform its intended functi ...
** the
Lagrange multiplier In mathematical optimization, the method of Lagrange multipliers is a strategy for finding the local maxima and minima of a function (mathematics), function subject to constraint (mathematics), equation constraints (i.e., subject to the conditio ...
in
mathematical optimization Mathematical optimization (alternatively spelled ''optimisation'') or mathematical programming is the selection of a best element, with regard to some criteria, from some set of available alternatives. It is generally divided into two subfiel ...
, known as the shadow price in economics ** the
Lebesgue measure In measure theory, a branch of mathematics, the Lebesgue measure, named after French mathematician Henri Lebesgue, is the standard way of assigning a measure to subsets of higher dimensional Euclidean '-spaces. For lower dimensions or , it c ...
denotes the volume or measure of a Lebesgue measurable set **
longitude Longitude (, ) is a geographic coordinate that specifies the east- west position of a point on the surface of the Earth, or another celestial body. It is an angular measurement, usually expressed in degrees and denoted by the Greek lett ...
in
geodesy Geodesy or geodetics is the science of measuring and representing the Figure of the Earth, geometry, Gravity of Earth, gravity, and Earth's rotation, spatial orientation of the Earth in Relative change, temporally varying Three-dimensional spac ...
** linear density ** ecliptic longitude in
astronomy Astronomy is a natural science that studies celestial objects and the phenomena that occur in the cosmos. It uses mathematics, physics, and chemistry in order to explain their origin and their overall evolution. Objects of interest includ ...
** the Liouville function in
number theory Number theory is a branch of pure mathematics devoted primarily to the study of the integers and arithmetic functions. Number theorists study prime numbers as well as the properties of mathematical objects constructed from integers (for example ...
** the Carmichael function in
number theory Number theory is a branch of pure mathematics devoted primarily to the study of the integers and arithmetic functions. Number theorists study prime numbers as well as the properties of mathematical objects constructed from integers (for example ...
** the
empty string In formal language theory, the empty string, or empty word, is the unique String (computer science), string of length zero. Formal theory Formally, a string is a finite, ordered sequence of character (symbol), characters such as letters, digits ...
in
formal grammar A formal grammar is a set of Terminal and nonterminal symbols, symbols and the Production (computer science), production rules for rewriting some of them into every possible string of a formal language over an Alphabet (formal languages), alphabe ...
** a formal system (
lambda calculus In mathematical logic, the lambda calculus (also written as ''λ''-calculus) is a formal system for expressing computability, computation based on function Abstraction (computer science), abstraction and function application, application using var ...
) in mathematical logic **
thermal conductivity The thermal conductivity of a material is a measure of its ability to heat conduction, conduct heat. It is commonly denoted by k, \lambda, or \kappa and is measured in W·m−1·K−1. Heat transfer occurs at a lower rate in materials of low ...
** the
Lorentz transformation In physics, the Lorentz transformations are a six-parameter family of Linear transformation, linear coordinate transformation, transformations from a Frame of Reference, coordinate frame in spacetime to another frame that moves at a constant vel ...


Μμ (mu)

* \mu represents: ** the Möbius function in
number theory Number theory is a branch of pure mathematics devoted primarily to the study of the integers and arithmetic functions. Number theorists study prime numbers as well as the properties of mathematical objects constructed from integers (for example ...
** the population
mean A mean is a quantity representing the "center" of a collection of numbers and is intermediate to the extreme values of the set of numbers. There are several kinds of means (or "measures of central tendency") in mathematics, especially in statist ...
or
expected value In probability theory, the expected value (also called expectation, expectancy, expectation operator, mathematical expectation, mean, expectation value, or first Moment (mathematics), moment) is a generalization of the weighted average. Informa ...
in
probability Probability is a branch of mathematics and statistics concerning events and numerical descriptions of how likely they are to occur. The probability of an event is a number between 0 and 1; the larger the probability, the more likely an e ...
and
statistics Statistics (from German language, German: ', "description of a State (polity), state, a country") is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data. In applying statistics to a s ...
** a measure in
measure theory In mathematics, the concept of a measure is a generalization and formalization of geometrical measures (length, area, volume) and other common notions, such as magnitude (mathematics), magnitude, mass, and probability of events. These seemingl ...
**
micro- ''Micro'' (Greek letter μ, Mu (letter), mu, non-Italic type, italic) is a metric prefix, unit prefix in the metric system denoting a factor of one millionth (10−6). It comes from the Ancient Greek, Greek word (), meaning "small". It is the ...
, an
SI prefix The International System of Units, internationally known by the abbreviation SI (from French ), is the modern form of the metric system and the world's most widely used system of measurement. It is the only system of measurement with official st ...
denoting 10−6 (one millionth) **
Micrometre The micrometre (English in the Commonwealth of Nations, Commonwealth English as used by the International Bureau of Weights and Measures; SI symbol: μm) or micrometer (American English), also commonly known by the non-SI term micron, is a uni ...
or micron (retired in 1967 as a standalone symbol, replaced by "μm" using the standard SI meaning) ** the coefficient of friction in
physics Physics is the scientific study of matter, its Elementary particle, fundamental constituents, its motion and behavior through space and time, and the related entities of energy and force. "Physical science is that department of knowledge whi ...
** the service rate in
queueing theory Queueing theory is the mathematical study of waiting lines, or queues. A queueing model is constructed so that queue lengths and waiting time can be predicted. Queueing theory is generally considered a branch of operations research because th ...
** the dynamic viscosity in physics ** magnetic permeability in electromagnetics ** a muon ** reduced mass ** the ion mobility in plasma physics ** the Standard gravitational parameter in
celestial mechanics Celestial mechanics is the branch of astronomy that deals with the motions of objects in outer space. Historically, celestial mechanics applies principles of physics (classical mechanics) to astronomical objects, such as stars and planets, to ...
** population mean in
statistics Statistics (from German language, German: ', "description of a State (polity), state, a country") is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data. In applying statistics to a s ...
**
chemical potential In thermodynamics, the chemical potential of a Chemical specie, species is the energy that can be absorbed or released due to a change of the particle number of the given species, e.g. in a chemical reaction or phase transition. The chemical potent ...
in
thermodynamics Thermodynamics is a branch of physics that deals with heat, Work (thermodynamics), work, and temperature, and their relation to energy, entropy, and the physical properties of matter and radiation. The behavior of these quantities is governed b ...
** Absorption coefficient ** Amplification factor **
Magnetic moment In electromagnetism, the magnetic moment or magnetic dipole moment is the combination of strength and orientation of a magnet or other object or system that exerts a magnetic field. The magnetic dipole moment of an object determines the magnitude ...
of a dipole


Νν (nu)

* \nu represents: **
frequency Frequency is the number of occurrences of a repeating event per unit of time. Frequency is an important parameter used in science and engineering to specify the rate of oscillatory and vibratory phenomena, such as mechanical vibrations, audio ...
in physics in
hertz The hertz (symbol: Hz) is the unit of frequency in the International System of Units (SI), often described as being equivalent to one event (or Cycle per second, cycle) per second. The hertz is an SI derived unit whose formal expression in ter ...
(Hz) ** Poisson's ratio in materials science ** a
neutrino A neutrino ( ; denoted by the Greek letter ) is an elementary particle that interacts via the weak interaction and gravity. The neutrino is so named because it is electrically neutral and because its rest mass is so small ('' -ino'') that i ...
** kinematic viscosity of liquids ** stoichiometric coefficient in chemistry ** true anomaly in
celestial mechanics Celestial mechanics is the branch of astronomy that deals with the motions of objects in outer space. Historically, celestial mechanics applies principles of physics (classical mechanics) to astronomical objects, such as stars and planets, to ...
**
degrees of freedom In many scientific fields, the degrees of freedom of a system is the number of parameters of the system that may vary independently. For example, a point in the plane has two degrees of freedom for translation: its two coordinates; a non-infinite ...
in
statistics Statistics (from German language, German: ', "description of a State (polity), state, a country") is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data. In applying statistics to a s ...
** the matching number of a graph ** the
p-adic valuation In number theory, the valuation or -adic order of an integer is the exponent of the highest power of the prime number that divides . It is denoted \nu_p(n). Equivalently, \nu_p(n) is the exponent to which p appears in the prime factorization of ...
of a number


Ξξ (xi)

* \Xi represents: ** the original Riemann Xi function, i.e. Riemann's lower case ξ, as denoted by Edmund Landau and currently ** the xi baryon * \xi represents: ** the original Riemann Xi function ** the modified definition of Riemann xi function, as denoted by Edmund Landau ** the extent of reaction


Οο (omicron)


Ππ (pi)

* \Pi represents: ** the product operator in mathematics ** a plane ** the unary projection operation in
relational algebra In database theory, relational algebra is a theory that uses algebraic structures for modeling data and defining queries on it with well founded semantics (computer science), semantics. The theory was introduced by Edgar F. Codd. The main applica ...
** the Pi function, i.e. the
Gamma function In mathematics, the gamma function (represented by Γ, capital Greek alphabet, Greek letter gamma) is the most common extension of the factorial function to complex numbers. Derived by Daniel Bernoulli, the gamma function \Gamma(z) is defined ...
when offset to coincide with the factorial ** the complete elliptic integral of the third kind ** the fundamental groupoid **
osmotic pressure Osmotic pressure is the minimum pressure which needs to be applied to a Solution (chemistry), solution to prevent the inward flow of its pure solvent across a semipermeable membrane. It is also defined as the measure of the tendency of a soluti ...
* \pi represents: ** Archimedes' constant (more commonly just called Pi), the ratio of a
circle A circle is a shape consisting of all point (geometry), points in a plane (mathematics), plane that are at a given distance from a given point, the Centre (geometry), centre. The distance between any point of the circle and the centre is cal ...
's
circumference In geometry, the circumference () is the perimeter of a circle or ellipse. The circumference is the arc length of the circle, as if it were opened up and straightened out to a line segment. More generally, the perimeter is the curve length arou ...
to its
diameter In geometry, a diameter of a circle is any straight line segment that passes through the centre of the circle and whose endpoints lie on the circle. It can also be defined as the longest Chord (geometry), chord of the circle. Both definitions a ...
** the prime-counting function ** the state distribution of a
Markov chain In probability theory and statistics, a Markov chain or Markov process is a stochastic process describing a sequence of possible events in which the probability of each event depends only on the state attained in the previous event. Informally ...
** in
reinforcement learning Reinforcement learning (RL) is an interdisciplinary area of machine learning and optimal control concerned with how an intelligent agent should take actions in a dynamic environment in order to maximize a reward signal. Reinforcement learnin ...
, a policy function defining how a software agent behaves for each possible state of its environment ** a type of
covalent bond A covalent bond is a chemical bond that involves the sharing of electrons to form electron pairs between atoms. These electron pairs are known as shared pairs or bonding pairs. The stable balance of attractive and repulsive forces between atom ...
in chemistry (
pi bond In chemistry, pi bonds (π bonds) are covalent chemical bonds, in each of which two lobes of an orbital on one atom overlap with two lobes of an orbital on another atom, and in which this overlap occurs laterally. Each of these atomic orbital ...
) ** a
pion In particle physics, a pion (, ) or pi meson, denoted with the Greek alphabet, Greek letter pi (letter), pi (), is any of three subatomic particles: , , and . Each pion consists of a quark and an antiquark and is therefore a meson. Pions are the ...
(pi meson) in particle physics ** in
statistics Statistics (from German language, German: ', "description of a State (polity), state, a country") is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data. In applying statistics to a s ...
, the population proportion ** nucleotide diversity in molecular genetics ** in electronics, a special type of small-signal model is referred to as a hybrid-pi model ** in discrete mathematics, a
permutation In mathematics, a permutation of a set can mean one of two different things: * an arrangement of its members in a sequence or linear order, or * the act or process of changing the linear order of an ordered set. An example of the first mean ...
** Projection * ϖ (a graphic variant, see pomega) represents: **
angular frequency In physics, angular frequency (symbol ''ω''), also called angular speed and angular rate, is a scalar measure of the angle rate (the angle per unit time) or the temporal rate of change of the phase argument of a sinusoidal waveform or sine ...
of a
wave In physics, mathematics, engineering, and related fields, a wave is a propagating dynamic disturbance (change from List of types of equilibrium, equilibrium) of one or more quantities. ''Periodic waves'' oscillate repeatedly about an equilibrium ...
, in
fluid dynamics In physics, physical chemistry and engineering, fluid dynamics is a subdiscipline of fluid mechanics that describes the flow of fluids – liquids and gases. It has several subdisciplines, including (the study of air and other gases in motion ...
(angular frequency is usually represented by \omega but this may be confused with vorticity in a fluid dynamics context) ** longitude of pericenter, in
astronomy Astronomy is a natural science that studies celestial objects and the phenomena that occur in the cosmos. It uses mathematics, physics, and chemistry in order to explain their origin and their overall evolution. Objects of interest includ ...
** comoving distance, in cosmology


Ρρ (rho)

* \Rho represents: ** one of the Gegenbauer functions in analytic number theory (may be replaced by the capital form of the Latin letter P). * \rho represents: ** one of the Gegenbauer functions in analytic number theory. ** the Dickman–de Bruijn function ** the
radius In classical geometry, a radius (: radii or radiuses) of a circle or sphere is any of the line segments from its Centre (geometry), center to its perimeter, and in more modern usage, it is also their length. The radius of a regular polygon is th ...
in a polar, cylindrical, or
spherical coordinate system In mathematics, a spherical coordinate system specifies a given point in three-dimensional space by using a distance and two angles as its three coordinates. These are * the radial distance along the line connecting the point to a fixed point ...
** the
correlation coefficient A correlation coefficient is a numerical measure of some type of linear correlation, meaning a statistical relationship between two variables. The variables may be two columns of a given data set of observations, often called a sample, or two c ...
in
statistics Statistics (from German language, German: ', "description of a State (polity), state, a country") is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data. In applying statistics to a s ...
** the radius of convergence in
real analysis In mathematics, the branch of real analysis studies the behavior of real numbers, sequences and series of real numbers, and real functions. Some particular properties of real-valued sequences and functions that real analysis studies include co ...
** the sensitivity to interest rate in
mathematical finance Mathematical finance, also known as quantitative finance and financial mathematics, is a field of applied mathematics, concerned with mathematical modeling in the financial field. In general, there exist two separate branches of finance that req ...
**
density Density (volumetric mass density or specific mass) is the ratio of a substance's mass to its volume. The symbol most often used for density is ''ρ'' (the lower case Greek letter rho), although the Latin letter ''D'' (or ''d'') can also be u ...
(mass or charge per unit volume; may be replaced by the capital form of the Latin letter D) ** resistivity ** the shape and reshape operators in APL (in the form ⍴) ** the rename operator in
relational algebra In database theory, relational algebra is a theory that uses algebraic structures for modeling data and defining queries on it with well founded semantics (computer science), semantics. The theory was introduced by Edgar F. Codd. The main applica ...
** the plastic ratio ** Rho meson


Σσς (sigma)

* \Sigma represents: ** the
summation In mathematics, summation is the addition of a sequence of numbers, called ''addends'' or ''summands''; the result is their ''sum'' or ''total''. Beside numbers, other types of values can be summed as well: functions, vectors, matrices, pol ...
operator ** the covariance matrix ** the set of terminal symbols in a
formal grammar A formal grammar is a set of Terminal and nonterminal symbols, symbols and the Production (computer science), production rules for rewriting some of them into every possible string of a formal language over an Alphabet (formal languages), alphabe ...
** Mathematical surface ** Sigma baryon * \sigma represents: ** Stefan–Boltzmann constant in blackbody radiation ** the divisor function in
number theory Number theory is a branch of pure mathematics devoted primarily to the study of the integers and arithmetic functions. Number theorists study prime numbers as well as the properties of mathematical objects constructed from integers (for example ...
** the
real part In mathematics, a complex number is an element of a number system that extends the real numbers with a specific element denoted , called the imaginary unit and satisfying the equation i^= -1; every complex number can be expressed in the form ...
of the
complex Complex commonly refers to: * Complexity, the behaviour of a system whose components interact in multiple ways so possible interactions are difficult to describe ** Complex system, a system composed of many components which may interact with each ...
variable s = \sigma + i t in
analytic number theory In mathematics, analytic number theory is a branch of number theory that uses methods from mathematical analysis to solve problems about the integers. It is often said to have begun with Peter Gustav Lejeune Dirichlet's 1837 introduction of Dir ...
** the sign of a
permutation In mathematics, a permutation of a set can mean one of two different things: * an arrangement of its members in a sequence or linear order, or * the act or process of changing the linear order of an ordered set. An example of the first mean ...
in the theory of finite groups ** the population
standard deviation In statistics, the standard deviation is a measure of the amount of variation of the values of a variable about its Expected value, mean. A low standard Deviation (statistics), deviation indicates that the values tend to be close to the mean ( ...
, a measure of spread in
probability Probability is a branch of mathematics and statistics concerning events and numerical descriptions of how likely they are to occur. The probability of an event is a number between 0 and 1; the larger the probability, the more likely an e ...
and
statistics Statistics (from German language, German: ', "description of a State (polity), state, a country") is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data. In applying statistics to a s ...
** a type of
covalent bond A covalent bond is a chemical bond that involves the sharing of electrons to form electron pairs between atoms. These electron pairs are known as shared pairs or bonding pairs. The stable balance of attractive and repulsive forces between atom ...
in chemistry (
sigma bond In chemistry, sigma bonds (σ bonds) or sigma overlap are the strongest type of covalent chemical bond. They are formed by head-on overlapping between atomic orbitals along the internuclear axis. Sigma bonding is most simply defined for diat ...
) ** the selection operator in
relational algebra In database theory, relational algebra is a theory that uses algebraic structures for modeling data and defining queries on it with well founded semantics (computer science), semantics. The theory was introduced by Edgar F. Codd. The main applica ...
** stress in mechanics **
electrical conductivity Electrical resistivity (also called volume resistivity or specific electrical resistance) is a fundamental specific property of a material that measures its electrical resistance or how strongly it resists electric current. A low resistivity in ...
** area density ** Cross section *** nuclear cross section ** surface charge density for microparticles **
standard deviation In statistics, the standard deviation is a measure of the amount of variation of the values of a variable about its Expected value, mean. A low standard Deviation (statistics), deviation indicates that the values tend to be close to the mean ( ...
of a
random variable A random variable (also called random quantity, aleatory variable, or stochastic variable) is a Mathematics, mathematical formalization of a quantity or object which depends on randomness, random events. The term 'random variable' in its mathema ...
in
statistics Statistics (from German language, German: ', "description of a State (polity), state, a country") is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data. In applying statistics to a s ...
** Spectrum of a matrix ** Spin


Ττ (tau)

* \tau represents: **
torque In physics and mechanics, torque is the rotational analogue of linear force. It is also referred to as the moment of force (also abbreviated to moment). The symbol for torque is typically \boldsymbol\tau, the lowercase Greek letter ''tau''. Wh ...
, the net rotational force in
mechanics Mechanics () is the area of physics concerned with the relationships between force, matter, and motion among Physical object, physical objects. Forces applied to objects may result in Displacement (vector), displacements, which are changes of ...
** the elementary tau lepton in
particle physics Particle physics or high-energy physics is the study of Elementary particle, fundamental particles and fundamental interaction, forces that constitute matter and radiation. The field also studies combinations of elementary particles up to the s ...
** a mean lifetime, of an
exponential decay A quantity is subject to exponential decay if it decreases at a rate proportional to its current value. Symbolically, this process can be expressed by the following differential equation, where is the quantity and (lambda Lambda (; uppe ...
or
spontaneous emission Spontaneous emission is the process in which a Quantum mechanics, quantum mechanical system (such as a molecule, an atom or a subatomic particle) transits from an excited state, excited energy state to a lower energy state (e.g., its ground state ...
process ** the
time constant In physics and engineering, the time constant, usually denoted by the Greek language, Greek letter (tau), is the parameter characterizing the response to a step input of a first-order, LTI system theory, linear time-invariant (LTI) system.Concre ...
of any device, such as an RC circuit **
proper time In relativity, proper time (from Latin, meaning ''own time'') along a timelike world line is defined as the time as measured by a clock following that line. The proper time interval between two events on a world line is the change in proper time ...
in relativity ** one turn: the constant ratio of a
circle A circle is a shape consisting of all point (geometry), points in a plane (mathematics), plane that are at a given distance from a given point, the Centre (geometry), centre. The distance between any point of the circle and the centre is cal ...
's
circumference In geometry, the circumference () is the perimeter of a circle or ellipse. The circumference is the arc length of the circle, as if it were opened up and straightened out to a line segment. More generally, the perimeter is the curve length arou ...
to its
radius In classical geometry, a radius (: radii or radiuses) of a circle or sphere is any of the line segments from its Centre (geometry), center to its perimeter, and in more modern usage, it is also their length. The radius of a regular polygon is th ...
, with value 2\pi (6.283...). ** Kendall tau rank correlation coefficient, a measure of
rank correlation In statistics, a rank correlation is any of several statistics that measure an ordinal association — the relationship between rankings of different ordinal data, ordinal variables or different rankings of the same variable, where a "ranking" is t ...
in statistics ** Ramanujan's tau function in
number theory Number theory is a branch of pure mathematics devoted primarily to the study of the integers and arithmetic functions. Number theorists study prime numbers as well as the properties of mathematical objects constructed from integers (for example ...
**
shear stress Shear stress (often denoted by , Greek alphabet, Greek: tau) is the component of stress (physics), stress coplanar with a material cross section. It arises from the shear force, the component of force vector parallel to the material cross secti ...
in
continuum mechanics Continuum mechanics is a branch of mechanics that deals with the deformation of and transmission of forces through materials modeled as a ''continuous medium'' (also called a ''continuum'') rather than as discrete particles. Continuum mec ...
** a type variable in type theories, such as the
simply typed lambda calculus The simply typed lambda calculus (), a form of type theory, is a typed interpretation of the lambda calculus with only one type constructor () that builds function types. It is the canonical and simplest example of a typed lambda calculus. The ...
** path tortuosity in reservoir engineering ** in
topology Topology (from the Greek language, Greek words , and ) is the branch of mathematics concerned with the properties of a Mathematical object, geometric object that are preserved under Continuous function, continuous Deformation theory, deformat ...
, a given topology ** the
tau Tau (; uppercase Τ, lowercase τ or \boldsymbol\tau; ) is the nineteenth letter of the Greek alphabet, representing the voiceless alveolar plosive, voiceless dental or alveolar plosive . In the system of Greek numerals, it has a value of 300 ...
in
biochemistry Biochemistry, or biological chemistry, is the study of chemical processes within and relating to living organisms. A sub-discipline of both chemistry and biology, biochemistry may be divided into three fields: structural biology, enzymology, a ...
, a
protein Proteins are large biomolecules and macromolecules that comprise one or more long chains of amino acid residue (biochemistry), residues. Proteins perform a vast array of functions within organisms, including Enzyme catalysis, catalysing metab ...
associated to
microtubule Microtubules are polymers of tubulin that form part of the cytoskeleton and provide structure and shape to eukaryotic cells. Microtubules can be as long as 50 micrometres, as wide as 23 to 27 nanometer, nm and have an inner diameter bet ...
s ** the number of divisors of highly composite numbers ** precision (\tau^2), the reciprocal of
variance In probability theory and statistics, variance is the expected value of the squared deviation from the mean of a random variable. The standard deviation (SD) is obtained as the square root of the variance. Variance is a measure of dispersion ...
, in
statistics Statistics (from German language, German: ', "description of a State (polity), state, a country") is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data. In applying statistics to a s ...


ϒυ (upsilon)

* \Upsilon (U+03D2) represents: ** the upsilon meson


Φφ (phi)

* \Phi represents: ** the work function in physics; the energy required by a photon to remove an electron from the surface of a metal ** magnetic flux or electric flux ** the
cumulative distribution function In probability theory and statistics, the cumulative distribution function (CDF) of a real-valued random variable X, or just distribution function of X, evaluated at x, is the probability that X will take a value less than or equal to x. Ever ...
of the
normal distribution In probability theory and statistics, a normal distribution or Gaussian distribution is a type of continuous probability distribution for a real-valued random variable. The general form of its probability density function is f(x) = \frac ...
in statistics ** phenyl functional group in organic chemistry ( pseudoelement symbol) ** the reciprocal of the
golden ratio In mathematics, two quantities are in the golden ratio if their ratio is the same as the ratio of their summation, sum to the larger of the two quantities. Expressed algebraically, for quantities and with , is in a golden ratio to if \fr ...
(represented by \phi, below), also represented as 1/\phi ** the value of the integration of information in a system (based on integrated information theory) ** Geopotential ** Alternative symbol for a
wave function In quantum physics, a wave function (or wavefunction) is a mathematical description of the quantum state of an isolated quantum system. The most common symbols for a wave function are the Greek letters and (lower-case and capital psi (letter) ...
in
quantum mechanics Quantum mechanics is the fundamental physical Scientific theory, theory that describes the behavior of matter and of light; its unusual characteristics typically occur at and below the scale of atoms. Reprinted, Addison-Wesley, 1989, It is ...
Note: The
empty set In mathematics, the empty set or void set is the unique Set (mathematics), set having no Element (mathematics), elements; its size or cardinality (count of elements in a set) is 0, zero. Some axiomatic set theories ensure that the empty set exi ...
symbol ∅ looks similar, but is unrelated to the Greek letter. * \phi or \varphi represents: ** the
golden ratio In mathematics, two quantities are in the golden ratio if their ratio is the same as the ratio of their summation, sum to the larger of the two quantities. Expressed algebraically, for quantities and with , is in a golden ratio to if \fr ...
1.618... in mathematics, art, and architecture **
Euler's totient function In number theory, Euler's totient function counts the positive integers up to a given integer that are relatively prime to . It is written using the Greek letter phi as \varphi(n) or \phi(n), and may also be called Euler's phi function. In ot ...
in number theory ** the argument of a
complex number In mathematics, a complex number is an element of a number system that extends the real numbers with a specific element denoted , called the imaginary unit and satisfying the equation i^= -1; every complex number can be expressed in the for ...
in mathematics ** the value of a plane angle in physics and mathematics ** the
angle In Euclidean geometry, an angle can refer to a number of concepts relating to the intersection of two straight Line (geometry), lines at a Point (geometry), point. Formally, an angle is a figure lying in a Euclidean plane, plane formed by two R ...
to the ''z'' axis in spherical coordinates (mathematics) ** epoch or phase difference between two waves or vectors ** the
angle In Euclidean geometry, an angle can refer to a number of concepts relating to the intersection of two straight Line (geometry), lines at a Point (geometry), point. Formally, an angle is a figure lying in a Euclidean plane, plane formed by two R ...
to the ''x'' axis in the ''xy''- plane in spherical or cylindrical coordinates (physics) **
latitude In geography, latitude is a geographic coordinate system, geographic coordinate that specifies the north-south position of a point on the surface of the Earth or another celestial body. Latitude is given as an angle that ranges from −90° at t ...
in
geodesy Geodesy or geodetics is the science of measuring and representing the Figure of the Earth, geometry, Gravity of Earth, gravity, and Earth's rotation, spatial orientation of the Earth in Relative change, temporally varying Three-dimensional spac ...
** radiant flux ** neutron flux **
Potential energy In physics, potential energy is the energy of an object or system due to the body's position relative to other objects, or the configuration of its particles. The energy is equal to the work done against any restoring forces, such as gravity ...
**
electric potential Electric potential (also called the ''electric field potential'', potential drop, the electrostatic potential) is defined as electric potential energy per unit of electric charge. More precisely, electric potential is the amount of work (physic ...
** a
scalar field In mathematics and physics, a scalar field is a function associating a single number to each point in a region of space – possibly physical space. The scalar may either be a pure mathematical number ( dimensionless) or a scalar physical ...
in
quantum field theory In theoretical physics, quantum field theory (QFT) is a theoretical framework that combines Field theory (physics), field theory and the principle of relativity with ideas behind quantum mechanics. QFT is used in particle physics to construct phy ...
** the
probability density function In probability theory, a probability density function (PDF), density function, or density of an absolutely continuous random variable, is a Function (mathematics), function whose value at any given sample (or point) in the sample space (the s ...
of the
normal distribution In probability theory and statistics, a normal distribution or Gaussian distribution is a type of continuous probability distribution for a real-valued random variable. The general form of its probability density function is f(x) = \frac ...
in statistics ** the Veblen functions


Χχ (chi)

* \chi represents: ** the
chi distribution In probability theory and statistics, the chi distribution is a continuous probability distribution over the non-negative real line. It is the distribution of the positive square root of a sum of squared independent Gaussian random variables. E ...
in
statistics Statistics (from German language, German: ', "description of a State (polity), state, a country") is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data. In applying statistics to a s ...
(\chi^2 is the more frequently encountered chi-squared distribution) ** the chromatic number of a graph in
graph theory In mathematics and computer science, graph theory is the study of ''graph (discrete mathematics), graphs'', which are mathematical structures used to model pairwise relations between objects. A graph in this context is made up of ''Vertex (graph ...
** the
Euler characteristic In mathematics, and more specifically in algebraic topology and polyhedral combinatorics, the Euler characteristic (or Euler number, or Euler–Poincaré characteristic) is a topological invariant, a number that describes a topological space's ...
in
algebraic topology Algebraic topology is a branch of mathematics that uses tools from abstract algebra to study topological spaces. The basic goal is to find algebraic invariant (mathematics), invariants that classification theorem, classify topological spaces up t ...
**
electronegativity Electronegativity, symbolized as , is the tendency for an atom of a given chemical element to attract shared electrons (or electron density) when forming a chemical bond. An atom's electronegativity is affected by both its atomic number and the ...
in the
periodic table The periodic table, also known as the periodic table of the elements, is an ordered arrangement of the chemical elements into rows (" periods") and columns (" groups"). It is an icon of chemistry and is widely used in physics and other s ...
** the Fourier transform of a linear response function ** a character in
mathematics Mathematics is a field of study that discovers and organizes methods, Mathematical theory, theories and theorems that are developed and Mathematical proof, proved for the needs of empirical sciences and mathematics itself. There are many ar ...
; especially a Dirichlet character in
number theory Number theory is a branch of pure mathematics devoted primarily to the study of the integers and arithmetic functions. Number theorists study prime numbers as well as the properties of mathematical objects constructed from integers (for example ...
** sometimes the
mole fraction In chemistry, the mole fraction or molar fraction, also called mole proportion or molar proportion, is a quantity defined as the ratio between the amount of a constituent substance, ''ni'' (expressed in unit of moles, symbol mol), and the to ...
** a characteristic or
indicator function In mathematics, an indicator function or a characteristic function of a subset of a set is a function that maps elements of the subset to one, and all other elements to zero. That is, if is a subset of some set , then the indicator functio ...
in mathematics ** the magnetic susceptibility of a material in physics ** the fission neutron energy spectrum in neutron transport


Ψψ (psi)

* \Psi represents: ** a quaternary combinator in combinatory logic ** a symbol for
psychology Psychology is the scientific study of mind and behavior. Its subject matter includes the behavior of humans and nonhumans, both consciousness, conscious and Unconscious mind, unconscious phenomena, and mental processes such as thoughts, feel ...
** the
wave function In quantum physics, a wave function (or wavefunction) is a mathematical description of the quantum state of an isolated quantum system. The most common symbols for a wave function are the Greek letters and (lower-case and capital psi (letter) ...
in the
Schrödinger equation The Schrödinger equation is a partial differential equation that governs the wave function of a non-relativistic quantum-mechanical system. Its discovery was a significant landmark in the development of quantum mechanics. It is named after E ...
of
quantum mechanics Quantum mechanics is the fundamental physical Scientific theory, theory that describes the behavior of matter and of light; its unusual characteristics typically occur at and below the scale of atoms. Reprinted, Addison-Wesley, 1989, It is ...
* \psi represents: ** the J/psi mesons in particle physics ** the stream function in fluid dynamics ** the reciprocal Fibonacci constant ** the second Chebyshev function in
number theory Number theory is a branch of pure mathematics devoted primarily to the study of the integers and arithmetic functions. Number theorists study prime numbers as well as the properties of mathematical objects constructed from integers (for example ...
** the polygamma function in
mathematics Mathematics is a field of study that discovers and organizes methods, Mathematical theory, theories and theorems that are developed and Mathematical proof, proved for the needs of empirical sciences and mathematics itself. There are many ar ...
** the supergolden ratio **In circadian physiology, ψ represents the phase relationship between a zeitgeber and a biological rhythm. **In
virology Virology is the Scientific method, scientific study of biological viruses. It is a subfield of microbiology that focuses on their detection, structure, classification and evolution, their methods of infection and exploitation of host (biology), ...
the ψ site is a viral packaging signal. **
Water potential Water potential is the potential energy of water per unit volume relative to pure water in reference conditions. Water potential quantifies the tendency of water to move from one area to another due to osmosis, gravity, mechanical pressure and mat ...
in movement of water between plant cells.


Ωω (omega)

* \Omega represents: ** Absolute infinite ** the
SI unit The International System of Units, internationally known by the abbreviation SI (from French ), is the modern form of the metric system and the world's most widely used system of units of measurement, system of measurement. It is the only system ...
measure of
electrical resistance The electrical resistance of an object is a measure of its opposition to the flow of electric current. Its reciprocal quantity is , measuring the ease with which an electric current passes. Electrical resistance shares some conceptual paral ...
, the ohm ** the right ascension of the ascending node (RAAN) or Longitude of the ascending node in
astronomy Astronomy is a natural science that studies celestial objects and the phenomena that occur in the cosmos. It uses mathematics, physics, and chemistry in order to explain their origin and their overall evolution. Objects of interest includ ...
and
orbital mechanics Orbital mechanics or astrodynamics is the application of ballistics and celestial mechanics to rockets, satellites, and other spacecraft. The motion of these objects is usually calculated from Newton's laws of motion and the law of universal ...
** the omega constant 0.5671432904097838729999686622... ** an asymptotic lower bound notation related to
big O notation Big ''O'' notation is a mathematical notation that describes the asymptotic analysis, limiting behavior of a function (mathematics), function when the Argument of a function, argument tends towards a particular value or infinity. Big O is a memb ...
** in
probability theory Probability theory or probability calculus is the branch of mathematics concerned with probability. Although there are several different probability interpretations, probability theory treats the concept in a rigorous mathematical manner by expre ...
and
statistical mechanics In physics, statistical mechanics is a mathematical framework that applies statistical methods and probability theory to large assemblies of microscopic entities. Sometimes called statistical physics or statistical thermodynamics, its applicati ...
, the support ** a solid angle ** the omega baryon ** the arithmetic function counting a number's prime factors counted with multiplicity ** the density parameter in
cosmology Cosmology () is a branch of physics and metaphysics dealing with the nature of the universe, the cosmos. The term ''cosmology'' was first used in English in 1656 in Thomas Blount's ''Glossographia'', with the meaning of "a speaking of the wo ...
** the first uncountable ordinal (also written as ω1) ** Chaitin's constant for a given computer program ** the vacuum state in
quantum field theory In theoretical physics, quantum field theory (QFT) is a theoretical framework that combines Field theory (physics), field theory and the principle of relativity with ideas behind quantum mechanics. QFT is used in particle physics to construct phy ...
* \omega represents: **
angular velocity In physics, angular velocity (symbol or \vec, the lowercase Greek letter omega), also known as the angular frequency vector,(UP1) is a pseudovector representation of how the angular position or orientation of an object changes with time, i ...
/ radian frequency (rad/sec) ** the argument of periapsis in
astronomy Astronomy is a natural science that studies celestial objects and the phenomena that occur in the cosmos. It uses mathematics, physics, and chemistry in order to explain their origin and their overall evolution. Objects of interest includ ...
and
orbital mechanics Orbital mechanics or astrodynamics is the application of ballistics and celestial mechanics to rockets, satellites, and other spacecraft. The motion of these objects is usually calculated from Newton's laws of motion and the law of universal ...
** a
complex Complex commonly refers to: * Complexity, the behaviour of a system whose components interact in multiple ways so possible interactions are difficult to describe ** Complex system, a system composed of many components which may interact with each ...
cube A cube or regular hexahedron is a three-dimensional space, three-dimensional solid object in geometry, which is bounded by six congruent square (geometry), square faces, a type of polyhedron. It has twelve congruent edges and eight vertices. It i ...
root of unity In mathematics, a root of unity is any complex number that yields 1 when exponentiation, raised to some positive integer power . Roots of unity are used in many branches of mathematics, and are especially important in number theory, the theory ...
— the other is \omega^2 — (used to describe various ways of calculating the
discrete Fourier transform In mathematics, the discrete Fourier transform (DFT) converts a finite sequence of equally-spaced Sampling (signal processing), samples of a function (mathematics), function into a same-length sequence of equally-spaced samples of the discre ...
) ** the differentiability class (''i.e.'' C^\omega) for functions that are infinitely differentiable because they are complex analytic ** the first infinite ordinal ** the omega meson ** the set of
natural number In mathematics, the natural numbers are the numbers 0, 1, 2, 3, and so on, possibly excluding 0. Some start counting with 0, defining the natural numbers as the non-negative integers , while others start with 1, defining them as the positive in ...
s in
set theory Set theory is the branch of mathematical logic that studies Set (mathematics), sets, which can be informally described as collections of objects. Although objects of any kind can be collected into a set, set theory – as a branch of mathema ...
(although \mathbb or N is more common in other areas of mathematics) ** an asymptotic dominant notation related to
big O notation Big ''O'' notation is a mathematical notation that describes the asymptotic analysis, limiting behavior of a function (mathematics), function when the Argument of a function, argument tends towards a particular value or infinity. Big O is a memb ...
** in
probability theory Probability theory or probability calculus is the branch of mathematics concerned with probability. Although there are several different probability interpretations, probability theory treats the concept in a rigorous mathematical manner by expre ...
, a possible outcome of an experiment ** the arithmetic function counting a number's distinct prime factors ** the symbol ϖ, a graphic variant of π, is sometimes construed as omega with a bar over it; see π ** the
unsaturated fat An unsaturated fat is a fat or fatty acid in which there is at least one double bond within the fatty acid chain. A fatty acid chain is Monounsaturated fat, monounsaturated if it contains one double bond, and polyunsaturated fat, polyunsaturated i ...
s nomenclature in biochemistry (e.g. ω−3 fatty acids) ** the first uncountable ordinal \omega_1 (also written as Ω) ** the clique number (number of vertices in a maximum clique) of a graph in
graph theory In mathematics and computer science, graph theory is the study of ''graph (discrete mathematics), graphs'', which are mathematical structures used to model pairwise relations between objects. A graph in this context is made up of ''Vertex (graph ...


See also

* Blackboard bold letters used in mathematics * English pronunciation of Greek letters * Latin letters used in mathematics, science, and engineering *
List of letters used in mathematics, science, and engineering Latin letters, Latin and Greek letters are used in mathematics, science, engineering, and other areas where mathematical notation is used as symbols for Mathematical constant, constants, special functions, and also conventionally for Variable (m ...
* Glossary of mathematical symbols *
Mathematical Alphanumeric Symbols Mathematical Alphanumeric Symbols is a Unicode block comprising styled forms of Latin alphabet, Latin and Greek alphabet, Greek letters and decimal numerical digit, digits that enable mathematicians to denote different notions with different l ...
(a
Unicode block A Unicode block is one of several contiguous ranges of numeric character codes (code points) of the Unicode character set that are defined by the Unicode Consortium for administrative and documentation purposes. Typically, proposals such as the ...
) *
Mathematical notation Mathematical notation consists of using glossary of mathematical symbols, symbols for representing operation (mathematics), operations, unspecified numbers, relation (mathematics), relations, and any other mathematical objects and assembling ...
*
Greek alphabet The Greek alphabet has been used to write the Greek language since the late 9th or early 8th century BC. It was derived from the earlier Phoenician alphabet, and is the earliest known alphabetic script to systematically write vowels as wel ...


References


External links


A pronunciation guide with audio

Greek alphabet letters onclick copy paste
{{DEFAULTSORT:Greek Letters Used In Mathematics, Science, And Engineering *