List Of Exponential Topics
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{{Short description, none This is a list of exponential topics, by Wikipedia page. See also
list of logarithm topics {{Short description, None This is a list of logarithm topics, by Wikipedia page. See also the list of exponential topics. * Acoustic power * Antilogarithm * Apparent magnitude * Baker's theorem * Bel * Benford's law * Binary logarithm * Bode plot ...
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Accelerating change In futures studies and the history of technology, accelerating change is the observed exponential nature of the rate of technological change in recent history, which may suggest faster and more profound change in the future and may or may not be ...
* Approximating natural exponents (log base e) * Artin–Hasse exponential *
Bacterial growth 250px, Growth is shown as ''L'' = log(numbers) where numbers is the number of colony forming units per ml, versus ''T'' (time.) Bacterial growth is proliferation of bacterium into two daughter cells, in a process called binary fission. Providing ...
* Baker–Campbell–Hausdorff formula *
Cell growth Cell growth refers to an increase in the total mass of a cell, including both cytoplasmic, nuclear and organelle volume. Cell growth occurs when the overall rate of cellular biosynthesis (production of biomolecules or anabolism) is greater than ...
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Barometric formula The barometric formula, sometimes called the ''exponential atmosphere'' or ''isothermal atmosphere'', is a formula used to model how the pressure (or density) of the air changes with altitude. The pressure drops approximately by 11.3 pascals pe ...
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Beer–Lambert law The Beer–Lambert law, also known as Beer's law, the Lambert–Beer law, or the Beer–Lambert–Bouguer law relates the attenuation of light to the properties of the material through which the light is travelling. The law is commonly applied t ...
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Characterizations of the exponential function In mathematics, the exponential function can be characterized in many ways. The following characterizations (definitions) are most common. This article discusses why each characterization makes sense, and why the characterizations are independent o ...
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Catenary In physics and geometry, a catenary (, ) is the curve that an idealized hanging chain or cable assumes under its own weight when supported only at its ends in a uniform gravitational field. The catenary curve has a U-like shape, superfici ...
* Compound interest *
De Moivre's formula In mathematics, de Moivre's formula (also known as de Moivre's theorem and de Moivre's identity) states that for any real number and integer it holds that :\big(\cos x + i \sin x\big)^n = \cos nx + i \sin nx, where is the imaginary unit (). ...
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Derivative of the exponential map In the theory of Lie groups, the exponential map is a map from the Lie algebra of a Lie group into . In case is a matrix Lie group, the exponential map reduces to the matrix exponential. The exponential map, denoted , is analytic and has as su ...
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Doléans-Dade exponential In stochastic calculus, the Doléans-Dade exponential or stochastic exponential of a semimartingale ''X'' is the unique strong solution of the stochastic differential equation dY_t = Y_\,dX_t,\quad\quad Y_0=1,where Y_ denotes the process of left lim ...
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Doubling time The doubling time is the time it takes for a population to double in size/value. It is applied to population growth, inflation, resource extraction, consumption of goods, compound interest, the volume of malignant tumours, and many other things th ...
* ''e''-folding *
Elimination half-life Biological half-life (also known as elimination half-life, pharmacologic half-life) is the time taken for concentration of a biological substance (such as a medication) to decrease from its maximum concentration ( Cmax) to half of Cmax in the bl ...
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Error exponent In information theory, the error exponent of a channel code or source code over the block length of the code is the rate at which the error probability decays exponentially with the block length of the code. Formally, it is defined as the limiting ...
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Euler's formula Euler's formula, named after Leonhard Euler, is a mathematical formula in complex analysis that establishes the fundamental relationship between the trigonometric functions and the complex exponential function. Euler's formula states that fo ...
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Euler's identity In mathematics, Euler's identity (also known as Euler's equation) is the equality e^ + 1 = 0 where : is Euler's number, the base of natural logarithms, : is the imaginary unit, which by definition satisfies , and : is pi, the ratio of the circ ...
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e (mathematical constant) The number , also known as Euler's number, is a mathematical constant approximately equal to 2.71828 that can be characterized in many ways. It is the base of the natural logarithms. It is the limit of as approaches infinity, an express ...
* Exponent *
Exponent bias In IEEE 754 floating-point numbers, the exponent is biased in the engineering sense of the word – the value stored is offset from the actual value by the exponent bias, also called a biased exponent. Biasing is done because exponents have to be ...
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Exponential (disambiguation) Exponential may refer to any of several mathematical topics related to exponentiation, including: *Exponential function, also: **Matrix exponential, the matrix analogue to the above *Exponential decay, decrease at a rate proportional to value *Expo ...
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Exponential backoff Exponential backoff is an algorithm that uses feedback to multiplicatively decrease the rate of some process, in order to gradually find an acceptable rate. These algorithms find usage in a wide range of systems and processes, with radio network ...
* Exponential decay *
Exponential dichotomy In the mathematical theory of dynamical systems, an exponential dichotomy is a property of an equilibrium point that extends the idea of hyperbolicity to non- autonomous systems. Definition If :\dot = A(t)\mathbf is a linear non-autonomous dynam ...
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Exponential discounting In economics exponential discounting is a specific form of the discount function, used in the analysis of choice over time (with or without uncertainty). Formally, exponential discounting occurs when total utility is given by :U(\_^)=\sum_^\del ...
* Exponential diophantine equation *
Exponential dispersion model In probability and statistics, the class of exponential dispersion models (EDM) is a set of probability distributions that represents a generalisation of the natural exponential family.Jørgensen, B. (1987). Exponential dispersion models (with dis ...
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Exponential distribution In probability theory and statistics, the exponential distribution is the probability distribution of the time between events in a Poisson point process, i.e., a process in which events occur continuously and independently at a constant average ...
* Exponential error *
Exponential factorial The exponential factorial is a positive integer ''n'' raised to the power of ''n'' − 1, which in turn is raised to the power of ''n'' − 2, and so on and so forth in a right-grouping manner. That is, : n^ The expon ...
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Exponential family In probability and statistics, an exponential family is a parametric set of probability distributions of a certain form, specified below. This special form is chosen for mathematical convenience, including the enabling of the user to calculate ...
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Exponential field In mathematics, an exponential field is a field that has an extra operation on its elements which extends the usual idea of exponentiation. Definition A field is an algebraic structure composed of a set of elements, ''F'', two binary operations, ...
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Exponential formula In combinatorial mathematics, the exponential formula (called the polymer expansion in physics) states that the exponential generating function for structures on finite sets is the exponential of the exponential generating function for connected st ...
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Exponential function The exponential function is a mathematical function denoted by f(x)=\exp(x) or e^x (where the argument is written as an exponent). Unless otherwise specified, the term generally refers to the positive-valued function of a real variable, a ...
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Exponential generating function In mathematics, a generating function is a way of encoding an infinite sequence of numbers () by treating them as the coefficients of a formal power series. This series is called the generating function of the sequence. Unlike an ordinary series ...
* Exponential-Golomb coding *
Exponential growth Exponential growth is a process that increases quantity over time. It occurs when the instantaneous rate of change (that is, the derivative) of a quantity with respect to time is proportional to the quantity itself. Described as a function, a q ...
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Exponential hierarchy In computational complexity theory, the exponential hierarchy is a hierarchy of complexity classes, which is an exponential time analogue of the polynomial hierarchy. As elsewhere in complexity theory, “exponential” is used in two different me ...
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Exponential integral In mathematics, the exponential integral Ei is a special function on the complex plane. It is defined as one particular definite integral of the ratio between an exponential function and its argument. Definitions For real non-zero values of  ...
* Exponential integrator * Exponential map (Lie theory) *
Exponential map (Riemannian geometry) In Riemannian geometry, an exponential map is a map from a subset of a tangent space T''p'M'' of a Riemannian manifold (or pseudo-Riemannian manifold) ''M'' to ''M'' itself. The (pseudo) Riemannian metric determines a canonical affine connect ...
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Exponential map (discrete dynamical systems) In the theory of dynamical systems, the exponential map can be used as the Dynamical system (definition), evolution function of Recurrence relation, the discrete nonlinear dynamical system. Family The family of exponential functions is called the ...
* Exponential notation *
Exponential object In mathematics, specifically in category theory, an exponential object or map object is the categorical generalization of a function space in set theory. Categories with all finite products and exponential objects are called cartesian closed c ...
(
category theory Category theory is a general theory of mathematical structures and their relations that was introduced by Samuel Eilenberg and Saunders Mac Lane in the middle of the 20th century in their foundational work on algebraic topology. Nowadays, cate ...
) * Exponential polynomials—see also
Touchard polynomials The Touchard polynomials, studied by , also called the exponential polynomials or Bell polynomials, comprise a polynomial sequence of binomial type defined by :T_n(x)=\sum_^n S(n,k)x^k=\sum_^n \left\x^k, where S(n,k)=\left\is a Stirling numbe ...
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combinatorics Combinatorics is an area of mathematics primarily concerned with counting, both as a means and an end in obtaining results, and certain properties of finite structures. It is closely related to many other areas of mathematics and has many appl ...
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Exponential response formula In mathematics, the exponential response formula (ERF), also known as exponential response and complex replacement, is a method used to find a particular solution of a non-homogeneous linear ordinary differential equation of any order. The expon ...
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Exponential sheaf sequence In mathematics, the exponential sheaf sequence is a fundamental short exact sequence of sheaves used in complex geometry. Let ''M'' be a complex manifold, and write ''O'M'' for the sheaf of holomorphic functions on ''M''. Let ''O'M''* be ...
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Exponential smoothing Exponential smoothing is a rule of thumb technique for smoothing time series data using the exponential window function. Whereas in the simple moving average the past observations are weighted equally, exponential functions are used to assign expo ...
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Exponential stability :''See Lyapunov stability, which gives a definition of asymptotic stability for more general dynamical systems. All exponentially stable systems are also asymptotically stable.'' In control theory, a continuous linear time-invariant system (LTI) ...
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Exponential sum In mathematics, an exponential sum may be a finite Fourier series (i.e. a trigonometric polynomial), or other finite sum formed using the exponential function, usually expressed by means of the function :e(x) = \exp(2\pi ix).\, Therefore, a typic ...
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Exponential time In computer science, the time complexity is the computational complexity that describes the amount of computer time it takes to run an algorithm. Time complexity is commonly estimated by counting the number of elementary operations performed by t ...
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Sub-exponential time In computer science, the time complexity is the computational complexity that describes the amount of computer time it takes to run an algorithm. Time complexity is commonly estimated by counting the number of elementary operations performed by ...
* Exponential tree *
Exponential type In complex analysis, a branch of mathematics, a holomorphic function is said to be of exponential type C if its growth is bounded by the exponential function ''e'C'', ''z'', for some real-valued constant ''C'' as , ''z'',  → ∞ ...
* Exponentially equivalent measures *
Exponentiating by squaring Exponentiation is a mathematical operation, written as , involving two numbers, the '' base'' and the ''exponent'' or ''power'' , and pronounced as " (raised) to the (power of) ". When is a positive integer, exponentiation corresponds to re ...
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Exponentiation Exponentiation is a mathematical operation, written as , involving two numbers, the '' base'' and the ''exponent'' or ''power'' , and pronounced as " (raised) to the (power of) ". When is a positive integer, exponentiation corresponds to re ...
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Fermat's Last Theorem In number theory, Fermat's Last Theorem (sometimes called Fermat's conjecture, especially in older texts) states that no three positive integers , , and satisfy the equation for any integer value of greater than 2. The cases and have been k ...
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Forgetting curve The forgetting curve hypothesizes the decline of memory retention in time. This curve shows how information is lost over time when there is no attempt to retain it. A related concept is the strength of memory that refers to the durability that m ...
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Gaussian function In mathematics, a Gaussian function, often simply referred to as a Gaussian, is a function of the base form f(x) = \exp (-x^2) and with parametric extension f(x) = a \exp\left( -\frac \right) for arbitrary real constants , and non-zero . It is ...
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Gudermannian function In mathematics, the Gudermannian function relates a hyperbolic angle measure \psi to a circular angle measure \phi called the ''gudermannian'' of \psi and denoted \operatorname\psi. The Gudermannian function reveals a close relationship betwee ...
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Half-exponential function In mathematics, a half-exponential function is a functional square root of an exponential function. That is, a function f such that f composed with itself results in an exponential function: f\bigl(f(x)\bigr) = ab^x, for some constants Impossibi ...
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Half-life Half-life (symbol ) is the time required for a quantity (of substance) to reduce to half of its initial value. The term is commonly used in nuclear physics to describe how quickly unstable atoms undergo radioactive decay or how long stable ato ...
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Hyperbolic function In mathematics, hyperbolic functions are analogues of the ordinary trigonometric functions, but defined using the hyperbola rather than the circle. Just as the points form a circle with a unit radius, the points form the right half of the u ...
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Inflation In economics, inflation is an increase in the general price level of goods and services in an economy. When the general price level rises, each unit of currency buys fewer goods and services; consequently, inflation corresponds to a reductio ...
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inflation rate In economics, inflation is an increase in the general price level of goods and services in an economy. When the general price level rises, each unit of currency buys fewer goods and services; consequently, inflation corresponds to a reductio ...
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Interest In finance and economics, interest is payment from a borrower or deposit-taking financial institution to a lender or depositor of an amount above repayment of the principal sum (that is, the amount borrowed), at a particular rate. It is distinct ...
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Lifetime (physics) A quantity is subject to exponential decay if it decreases at a rate Proportionality (mathematics), proportional to its current value. Symbolically, this process can be expressed by the following differential equation, where is the quantity and ...
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Limiting factor A limiting factor is a variable of a system that causes a noticeable change in output or another measure of a type of system. The limiting factor is in a pyramid shape of organisms going up from the producers to consumers and so on. A factor not l ...
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Lindemann–Weierstrass theorem In transcendental number theory, the Lindemann–Weierstrass theorem is a result that is very useful in establishing the transcendence of numbers. It states the following: In other words, the extension field \mathbb(e^, \dots, e^) has transce ...
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List of integrals of exponential functions The following is a list of integrals of exponential functions. For a complete list of integral functions, please see the list of integrals. Indefinite integral Indefinite integrals are antiderivative functions. A constant (the constant of inte ...
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List of integrals of hyperbolic functions The following is a list of integrals (anti-derivative functions) of hyperbolic functions. For a complete list of integral functions, see list of integrals. In all formulas the constant ''a'' is assumed to be nonzero, and ''C'' denotes the constan ...
* Lyapunov exponent *
Malthusian catastrophe Malthusianism is the idea that population growth is potentially exponential while the growth of the food supply or other resources is linear, which eventually reduces living standards to the point of triggering a population die off. This event, c ...
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Malthusian growth model A Malthusian growth model, sometimes called a simple exponential growth model, is essentially exponential growth based on the idea of the function being proportional to the speed to which the function grows. The model is named after Thomas Robert ...
* Marshall–Olkin exponential distribution *
Matrix exponential In mathematics, the matrix exponential is a matrix function on square matrices analogous to the ordinary exponential function. It is used to solve systems of linear differential equations. In the theory of Lie groups, the matrix exponential give ...
* Moore's law *
Nachbin's theorem In mathematics, in the area of complex analysis, Nachbin's theorem (named after Leopoldo Nachbin) is commonly used to establish a bound on the growth rates for an analytic function. This article provides a brief review of growth rates, includi ...
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Piano key frequencies This is a list of the fundamental frequencies in hertz (cycles per second) of the keys of a modern 88-key standard or 108-key extended piano in twelve-tone equal temperament, with the 49th key, the fifth A (called A4), tuned to 440 Hz (refe ...
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p-adic exponential function In mathematics, the -adic number system for any prime number  extends the ordinary arithmetic of the rational numbers in a different way from the extension of the rational number system to the real and complex number systems. The extension ...
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Power law In statistics, a power law is a Function (mathematics), functional relationship between two quantities, where a Relative change and difference, relative change in one quantity results in a proportional relative change in the other quantity, inde ...
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Proof that e is irrational The e (mathematical constant), number ''e'' was introduced by Jacob Bernoulli in 1683. More than half a century later, Leonhard Euler, Euler, who had been a student of Jacob's younger brother Johann Bernoulli, Johann, proved that ''e'' is Irratio ...
* Proof that e is transcendental *
Q-exponential In combinatorial mathematics, a ''q''-exponential is a ''q''-analog of the exponential function, namely the eigenfunction of a ''q''-derivative. There are many ''q''-derivatives, for example, the classical ''q''-derivative, the Askey-Wilson ...
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Radioactive decay Radioactive decay (also known as nuclear decay, radioactivity, radioactive disintegration, or nuclear disintegration) is the process by which an unstable atomic nucleus loses energy by radiation. A material containing unstable nuclei is consid ...
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Rule of 70 In finance, the rule of 72, the rule of 70 and the rule of 69.3 are methods for estimating an investment's doubling time. The rule number (e.g., 72) is divided by the interest percentage per period (usually years) to obtain the approximate number ...
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Rule of 72 In finance, the rule of 72, the rule of 70 and the rule of 69.3 are methods for estimating an investment's doubling time. The rule number (e.g., 72) is divided by the interest percentage per period (usually years) to obtain the approximate numb ...
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Scientific notation Scientific notation is a way of expressing numbers that are too large or too small (usually would result in a long string of digits) to be conveniently written in decimal form. It may be referred to as scientific form or standard index form, o ...
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Six exponentials theorem In mathematics, specifically transcendental number theory, the six exponentials theorem is a result that, given the right conditions on the exponents, guarantees the transcendence of at least one of a set of exponentials. Statement If ''x''1, ''x ...
* Spontaneous emission * Super-exponentiation *
Tetration In mathematics, tetration (or hyper-4) is an operation based on iterated, or repeated, exponentiation. There is no standard notation for tetration, though \uparrow \uparrow and the left-exponent ''xb'' are common. Under the definition as rep ...
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Versor In mathematics, a versor is a quaternion of norm one (a ''unit quaternion''). The word is derived from Latin ''versare'' = "to turn" with the suffix ''-or'' forming a noun from the verb (i.e. ''versor'' = "the turner"). It was introduced by Will ...
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Wilkie's theorem In mathematics, Wilkie's theorem is a result by Alex Wilkie about the theory of ordered fields with an exponential function, or equivalently about the geometric nature of exponential varieties. Formulations In terms of model theory, Wilkie's the ...
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Zenzizenzizenzic Zenzizenzizenzic is an obsolete form of mathematical notation representing the eighth power of a number (that is, the zenzizenzizenzic of ''x'' is ''x''8), dating from a time when powers were written out in words rather than as superscript numbers. ...
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Exponentials Exponential may refer to any of several mathematical topics related to exponentiation, including: *Exponential function, also: **Matrix exponential, the matrix analogue to the above * Exponential decay, decrease at a rate proportional to value *Exp ...
Exponential Exponential may refer to any of several mathematical topics related to exponentiation, including: *Exponential function, also: **Matrix exponential, the matrix analogue to the above * Exponential decay, decrease at a rate proportional to value *Exp ...