Xi is the 14th letter of the

Greek alphabet The Greek alphabet has been used to write the Greek language since the late 9th or early 8th century BCE. It is derived from the earlier Phoenician alphabet, and was the earliest known alphabetic script to have distinct letters for vowels as we ...

(uppercase Ξ, lowercase ξ; el, ξι), representing the voiceless

consonant cluster In linguistics, a consonant cluster, consonant sequence or consonant compound, is a group of consonants which have no intervening vowel. In English, for example, the groups and are consonant clusters in the word ''splits''. In the education fie ...

. It is pronounced in

Modern Greek Modern Greek (, , or , ''Kiní Neoellinikí Glóssa''), generally referred to by speakers simply as Greek (, ), refers collectively to the dialects of the Greek language spoken in the modern era, including the official standardized form of the ...

, and generally or in

English English usually refers to: * English language * English people English may also refer to: Peoples, culture, and language * ''English'', an adjective for something of, from, or related to England ** English national ide ...

. In the system of

Greek numerals Greek numerals, also known as Ionic, Ionian, Milesian, or Alexandrian numerals, are a system of writing numbers using the letters of the Greek alphabet. In modern Greece, they are still used for ordinal numbers and in contexts similar to tho ...

, it has a value of 60. Xi was derived from the Phoenician letter

samekh Samekh (Phoenician ''sāmek'' ; Hebrew ''samekh'' , Syriac ''semkaṯ'') is the fifteenth letter of the Semitic abjads, including the Hebrew alphabet. Samekh represents a voiceless alveolar fricative . Unlike most Semitic consonants, the pro ...

. Xi is distinct from the letter

chi Chi or CHI may refer to: Greek *Chi (letter), the Greek letter (uppercase Χ, lowercase χ); Chinese *Chi (length), ''Chi'' (length) (尺), a traditional unit of length, about ⅓ meter *Chi (mythology) (螭), a dragon *Chi (surname) (池, pin ...

, which gave its form to the Latin letter X.

Greek

Both in classical

Ancient Greek Ancient Greek includes the forms of the Greek language used in ancient Greece and the ancient world from around 1500 BC to 300 BC. It is often roughly divided into the following periods: Mycenaean Greek (), Dark Ages (), the Archaic peri ...

and in

, the letter Ξ represents the consonant cluster /ks/. In some archaic local variants of the Greek alphabet, this letter was missing. Instead, especially in the dialects of most of the Greek mainland and

Euboea Evia (, ; el, Εύβοια ; grc, Εὔβοια ) or Euboia (, ) is the second-largest Greek island in area and population, after Crete. It is separated from Boeotia in mainland Greece by the narrow Euripus Strait (only at its narrowest poin ...

, the cluster /ks/ was represented by Χ (which in classical Greek is

, used for ). Because this variant of the Greek alphabet was used in

Magna Graecia Magna Graecia (, ; , , grc, Μεγάλη Ἑλλάς, ', it, Magna Grecia) was the name given by the Romans to the coastal areas of Southern Italy in the present-day Italian regions of Calabria, Apulia, Basilicata, Campania and Sicily; these re ...

(the Greek colonies in

Sicily (man) it, Siciliana (woman) , population_note = , population_blank1_title = , population_blank1 = , demographics_type1 = Ethnicity , demographics1_footnotes = , demographi ...

and the southern part of the Italian peninsula), the

Latin alphabet The Latin alphabet or Roman alphabet is the collection of letters originally used by the ancient Romans to write the Latin language. Largely unaltered with the exception of extensions (such as diacritics), it used to write English and the o ...

borrowed Χ rather than Ξ as the Latin letter that represented the /ks/ cluster that was also present in Latin.

Cyrillic

The Xi was adopted into the

early Cyrillic alphabet The Early Cyrillic alphabet, also called classical Cyrillic or paleo-Cyrillic, is a writing system that was developed in the First Bulgarian Empire during the late 9th century on the basis of the Greek alphabet for the Slavic people living ...

, as the letter

ksi Olajide Olayinka Williams "JJ" Olatunji (born 19 June 1993), known professionally as KSI, is an English YouTuber and rapper. He is a co-founder and member of the British YouTube group known as the Sidemen. He is the CEO of Misfits Boxing and ...

(Ѯ, ѯ).

Mathematics and science

Uppercase

The uppercase letter Ξ is used as a symbol in various contexts.

Pure mathematics

Harish-Chandra's Ξ function In mathematical harmonic analysis, Harish-Chandra's ''Ξ'' function is a special spherical function on a semisimple Lie group, studied by . Harish-Chandra used it to define Harish-Chandra's Schwartz space. gives a detailed description of the pr ...

harmonic analysis Harmonic analysis is a branch of mathematics concerned with the representation of Function (mathematics), functions or signals as the Superposition principle, superposition of basic waves, and the study of and generalization of the notions of Fo ...

and

representation theory Representation theory is a branch of mathematics that studies abstract algebraic structures by ''representing'' their elements as linear transformations of vector spaces, and studies modules over these abstract algebraic structures. In essen ...

* The

Riemann Xi function In mathematics, the Riemann Xi function is a variant of the Riemann zeta function, and is defined so as to have a particularly simple functional equation. The function is named in honour of Bernhard Riemann. Definition Riemann's original lower-ca ...

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 Diric ...

and

complex analysis Complex analysis, traditionally known as the theory of functions of a complex variable, is the branch of mathematical analysis that investigates Function (mathematics), functions of complex numbers. It is helpful in many branches of mathemati ...

Physics

* The " cascade particles" in particle physics * The partition function under the

grand canonical ensemble In statistical mechanics, the grand canonical ensemble (also known as the macrocanonical ensemble) is the statistical ensemble that is used to represent the possible states of a mechanical system of particles that are in thermodynamic equilibrium ...

in statistical mechanics

Other uses

* Indicating "no change of state" in

Z notation The Z notation is a formal specification language used for describing and modelling computing systems. It is targeted at the clear specification of computer programs and computer-based systems in general. History In 1974, Jean-Raymond Abrial ...

computing Computing is any goal-oriented activity requiring, benefiting from, or creating computing machinery. It includes the study and experimentation of algorithmic processes, and development of both hardware and software. Computing has scientific, e ...

* Monetary units of the

cryptocurrencies A cryptocurrency, crypto-currency, or crypto is a digital currency designed to work as a medium of exchange through a computer network that is not reliant on any central authority, such as a government or bank A bank is a financial i ...

Ether In organic chemistry, ethers are a class of compounds that contain an ether group—an oxygen atom connected to two alkyl or aryl groups. They have the general formula , where R and R′ represent the alkyl or aryl groups. Ethers can again be c ...

(and less commonly

ETC * Etc. or et cetera, a Latin expression meaning "and the other things" or "and the rest". ETC or etc may also refer to: Companies and organizations * ETC (Chilean TV channel), a Chilean cable television channel * ETC (Philippine TV channel), a P ...

), equal to 10¹⁸ Wei

Lowercase

The lowercase letter ξ is used as a symbol for:

Pure mathematics

Random variable A random variable (also called random quantity, aleatory variable, or stochastic variable) is a mathematical formalization of a quantity or object which depends on random events. It is a mapping or a function from possible outcomes (e.g., the po ...

s * A parameter in a

generalized Pareto distribution In statistics, the generalized Pareto distribution (GPD) is a family of continuous probability distributions. It is often used to model the tails of another distribution. It is specified by three parameters: location \mu, scale \sigma, and shap ...

* The symmetric function equation of the

Riemann zeta function The Riemann zeta function or Euler–Riemann zeta function, denoted by the Greek letter (zeta), is a mathematical function of a complex variable defined as \zeta(s) = \sum_^\infty \frac = \frac + \frac + \frac + \cdots for \operatorname(s) > ...

in mathematics, also known as the

* A

universal set In set theory, a universal set is a set which contains all objects, including itself. In set theory as usually formulated, it can be proven in multiple ways that a universal set does not exist. However, some non-standard variants of set theory inc ...

set theory Set theory is the branch of mathematical logic that studies 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 mathematics, is mostly conce ...

* A number used in the remainder term of

Taylor's theorem In calculus, Taylor's theorem gives an approximation of a ''k''-times differentiable function around a given point by a polynomial of degree ''k'', called the ''k''th-order Taylor polynomial. For a smooth function, the Taylor polynomial is the t ...

that falls between the limits ''a'' and ''b'' * A number used in error approximations for formulas that are applications of Taylor's theorem, such as

Newton–Cotes formulas In numerical analysis, the Newton–Cotes formulas, also called the Newton–Cotes quadrature rules or simply Newton–Cotes rules, are a group of formulas for numerical integration (also called ''quadrature'') based on evaluating the integrand at ...

Physics and astronomy

* In fluid dynamics, the

Iribarren parameter In fluid dynamics, the Iribarren number or Iribarren parameter – also known as the surf similarity parameter and breaker parameter – is a dimensionless parameter used to model several effects of (breaking) surface gravity waves on beaches and ...

. * The

initial mass function In astronomy, the initial mass function (IMF) is an empirical function that describes the initial Frequency distribution, distribution of masses for a population of stars. The IMF is an output of the process of star formation. The IMF is often g ...

astronomy Astronomy () is a natural science that studies astronomical object, celestial objects and phenomena. It uses mathematics, physics, and chemistry in order to explain their origin and chronology of the Universe, evolution. Objects of interest ...

. * The

correlation function A correlation function is a function that gives the statistical correlation between random variables, contingent on the spatial or temporal distance between those variables. If one considers the correlation function between random variables rep ...

. *

Spatial frequency In mathematics, physics, and engineering, spatial frequency is a characteristic of any structure that is periodic across position in space. The spatial frequency is a measure of how often sinusoidal components (as determined by the Fourier tra ...

; also sometimes temporal

frequency Frequency is the number of occurrences of a repeating event per unit of time. It is also occasionally referred to as ''temporal frequency'' for clarity, and is distinct from ''angular frequency''. Frequency is measured in hertz (Hz) which is eq ...

. * A small displacement in MHD

plasma stability The stability of a plasma is an important consideration in the study of plasma physics. When a system containing a plasma is at equilibrium, it is possible for certain parts of the plasma to be disturbed by small perturbative forces acting on it ...

theory * The x-coordinate of computational space as used in

computational fluid dynamics Computational fluid dynamics (CFD) is a branch of fluid mechanics that uses numerical analysis and data structures to analyze and solve problems that involve fluid flows. Computers are used to perform the calculations required to simulate th ...

Potential difference Voltage, also known as electric pressure, electric tension, or (electric) potential difference, is the difference in electric potential between two points. In a static electric field, it corresponds to the work needed per unit of charge to m ...

in physics (in volts) * The radial integral in the spin-orbit matrix operator in

atomic physics Atomic physics is the field of physics that studies atoms as an isolated system of electrons and an atomic nucleus. Atomic physics typically refers to the study of atomic structure and the interaction between atoms. It is primarily concerned wit ...

. * The

Killing vector In mathematics, a Killing vector field (often called a Killing field), named after Wilhelm Killing, is a vector field on a Riemannian manifold (or pseudo-Riemannian manifold) that preserves the metric. Killing fields are the infinitesimal gene ...

in general relativity. * Average logarithmic energy decrement per collision (neutron calculations in nuclear physics) * Pippard's cohesion length in

superconductors Superconductivity is a set of physical properties observed in certain materials where electrical resistance vanishes and magnetic flux fields are expelled from the material. Any material exhibiting these properties is a superconductor. Unlike ...

* The diameter of a crystal nucleus in

nucleation In thermodynamics, nucleation is the first step in the formation of either a new thermodynamic phase or structure via self-assembly or self-organization within a substance or mixture. Nucleation is typically defined to be the process that deter ...

theory *

Microturbulence Microturbulence is a form of turbulence that varies over small distance scales. (Large-scale turbulence is called macroturbulence.) Stellar Microturbulence is one of several mechanisms that can cause broadening of the absorption lines in the st ...

velocity in a stellar atmosphere * The dimensionless longitudinal momentum loss of a beam particle after a two-body interaction in accelerator physics. * Dimensionless distance variable used in the

Lane–Emden equation In astrophysics, the Lane–Emden equation is a dimensionless form of Poisson's equation for the gravitational potential of a Newtonian self-gravitating, spherically symmetric, polytropic fluid. It is named after astrophysicists Jonathan Homer L ...

Other uses

* Propositional variables in some philosophical works, first found in Wittgenstein's Tractatus *

Extent of reaction In physical chemistry and chemical engineering, extent of reaction is a quantity that measures the extent to which the reaction has proceeded. Often, it refers specifically to the value of the extent of reaction when equilibrium has been reached. It ...

, a concept in

physical chemistry Physical chemistry is the study of macroscopic and microscopic phenomena in chemical systems in terms of the principles, practices, and concepts of physics such as motion, energy, force, time, thermodynamics, quantum chemistry, statistical mecha ...

used often in

chemical engineering Chemical engineering is an engineering field which deals with the study of operation and design of chemical plants as well as methods of improving production. Chemical engineers develop economical commercial processes to convert raw materials int ...

kinetics and

thermochemistry Thermochemistry is the study of the heat energy which is associated with chemical reactions and/or phase changes such as melting and boiling. A reaction may release or absorb energy, and a phase change may do the same. Thermochemistry focuses on ...

* Unknown

stereochemistry Stereochemistry, a subdiscipline of chemistry, involves the study of the relative spatial arrangement of atoms that form the structure of molecules and their manipulation. The study of stereochemistry focuses on the relationships between stereois ...

stereocentre In stereochemistry, a stereocenter of a molecule is an atom (center), axis or plane that is the focus of stereoisomerism; that is, when having at least three different groups bound to the stereocenter, interchanging any two different groups cr ...

configuration in a planar

ring system A ring system is a disc or ring, orbiting an astronomical object, that is composed of solid material such as dust and moonlets, and is a common component of satellite systems around giant planets. A ring system around a planet is also known as ...

organic chemistry Organic chemistry is a subdiscipline within chemistry involving the scientific study of the structure, properties, and reactions of organic compounds and organic materials, i.e., matter in its various forms that contain carbon atoms.Clayden, J.; ...

, as well as uppercase Xi for unknown ''R''/''S''/''E''/''Z'' configuration in general * One of the two different polypeptide chains of the human embryonic

hemoglobin Hemoglobin (haemoglobin BrE) (from the Greek word αἷμα, ''haîma'' 'blood' + Latin ''globus'' 'ball, sphere' + ''-in'') (), abbreviated Hb or Hgb, is the iron-containing oxygen-transport metalloprotein present in red blood cells (erythrocyte ...

types Hb-Portland (ξ₂γ₂) and Hb-Gower I (ξ₂ε₂) * A parameter denoted as

warped time Warp, warped or warping may refer to: Arts and entertainment Books and comics * WaRP Graphics, an alternative comics publisher * ''Warp'' (First Comics), comic book series published by First Comics based on the play ''Warp!'' * Warp (comics), a ...

used to derive the equations for homogeneous

azeotropic distillation In chemistry, azeotropic distillation is any of a range of techniques used to break an azeotrope in distillation. In chemical engineering, ''azeotropic distillation'' usually refers to the specific technique of adding another component to genera ...

* State Price Density in

mathematical finance Mathematical finance, also known as quantitative finance and financial mathematics, is a field of applied mathematics, concerned with mathematical modeling of financial markets. In general, there exist two separate branches of finance that require ...

* The information vector in the

Information Filter For statistics and control theory, Kalman filtering, also known as linear quadratic estimation (LQE), is an algorithm that uses a series of measurements observed over time, including statistical noise and other inaccuracies, and produces estima ...

GraphSLAM Simultaneous localization and mapping (SLAM) is the computational problem of constructing or updating a map of an unknown environment while simultaneously keeping track of an Intelligent agent, agent's location within it. While this initially ap ...

, and a number of other algorithms used for

robot localization Robot localization denotes the robot's ability to establish its own position and orientation within the frame of reference. Path planning is effectively an extension of localisation, in that it requires the determination of the robot's current pos ...

and

robotic mapping Robotic mapping is a discipline related to computer vision and cartography. The goal for an autonomous robot is to be able to construct (or use) a map (outdoor use) or floor plan (indoor use) and to localize itself and its recharging bases or be ...

. * Used in

Support Vector machines In machine learning, support vector machines (SVMs, also support vector networks) are supervised learning models with associated learning algorithms that analyze data for classification and regression analysis. Developed at AT&T Bell Laboratorie ...

in cases where the data is not

linearly separable In Euclidean geometry, linear separability is a property of two sets of point (geometry), points. This is most easily visualized in two dimensions (the Euclidean plane) by thinking of one set of points as being colored blue and the other set of poi ...

. * Used in

Microelectronics Microelectronics is a subfield of electronics. As the name suggests, microelectronics relates to the study and manufacture (or microfabrication) of very small electronic designs and components. Usually, but not always, this means micrometre-sc ...

to represent the distance from a p-n junction to a point in the

depletion region In semiconductor physics, the depletion region, also called depletion layer, depletion zone, junction region, space charge region or space charge layer, is an insulating region within a conductive, doped semiconductor material where the mobile ...

where the

electric field An electric field (sometimes E-field) is the physical field that surrounds electrically charged particles and exerts force on all other charged particles in the field, either attracting or repelling them. It also refers to the physical field fo ...

is strongest.

Character encodings

Greek Xi / Coptic Ksi

Unicode Code Charts
Greek and Coptic (Range: 0370-03FF)

Mathematical Xi

The following characters are used only as mathematical symbols. Stylized Greek text should be encoded using the normal Greek letters, with markup and formatting to indicate text style.

Other uses

*' Uppercase Ξ is used as an 'E' to stylise company names/logos like

Razer Razer may refer to: * Razer (Canadian TV channel), former name of MTV2, a Canadian digital television specialty service * Razer Inc., a Singaporean-American computer peripherals manufacturer specializing in PC gaming * Razer Phone, a smartphone desi ...

(styled as RΛZΞR), Tesla (styled as TΞSLA), musician

Banners A banner can be a flag or another piece of cloth bearing a symbol, logo, slogan or another message. A flag whose design is the same as the shield in a coat of arms (but usually in a square or rectangular shape) is called a banner of arms. Also ...

(styled as BANNΞRS), and in South Korean boy group ZE:A's newest logo (styled as "ZΞA") (Compare:

Heavy Metal umlaut A metal umlaut is a diacritic that is sometimes used gratuitously or decoratively over letters in the names of mainly hard rock or heavy metal music, heavy metal bands—for example, those of Blue Öyster Cult, Queensrÿche, Motörhead, the Accüs ...

; Faux Cyrillic)

References

{{DEFAULTSORT:Xi (Letter) Greek letters