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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 g of a Lie group G into G. In case G is a matrix Lie group, the exponential map reduces to the matrix exponential. The ex

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

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, incl

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 N is t

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

Exponentiation

Exponentiation is a mathematical operation, written as bn, involving two numbers, the base b and the exponent or power n, and pronounced as "b (raised) to the (power of) n". When n is a positive integ

Index of logarithm articles

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
* B

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-derivativ

Van der Corput's method

In mathematics, van der Corput's method generates estimates for exponential sums. The method applies two processes, the van der Corput processes A and B which relate the sums into simpler sums which a

Decimal antilogarithm

No description available.

Four exponentials conjecture

In mathematics, specifically the field of transcendental number theory, the four exponentials conjecture is a conjecture which, given the right conditions on the exponents, would guarantee the transce

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, The exponenti

Exponential minus 1

No description available.

Schanuel's conjecture

In mathematics, specifically transcendental number theory, Schanuel's conjecture is a conjecture made by Stephen Schanuel in the 1960s concerning the transcendence degree of certain field extensions o

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 theo

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.

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 functi

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 continuo

Tetration

In mathematics, tetration (or hyper-4) is an operation based on iterated, or repeated, exponentiation. There is no standard notation for tetration, though and the left-exponent xb are common. Under th

General antilogarithm

No description available.

Marshall–Olkin exponential distribution

In applied statistics, the Marshall–Olkin exponential distribution is any member of a certain family of continuous multivariate probability distributions with positive-valued components. It was introd

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

Binary antilogarithm

No description available.

List of representations of e

The mathematical constant e can be represented in a variety of ways as a real number. Since e is an irrational number (see proof that e is irrational), it cannot be represented as the quotient of two

Theory of fructification

In economics, the theory of fructification is a theory of the interest rate which was proposed by French economist and finance minister Anne Robert Jacques Turgot. The term theory of fructification is

Antilogarithm

No description available.

Growth curve (statistics)

The growth curve model in statistics is a specific multivariate linear model, also known as GMANOVA (Generalized Multivariate Analysis-Of-Variance). It generalizes MANOVA by allowing post-matrices, as

List of exponential topics

This is a list of exponential topics, by Wikipedia page. See also list of logarithm topics.
* Accelerating change
* Approximating natural exponents (log base e)
* Artin–Hasse exponential
* Bacteri

Exponential function

The exponential function is a mathematical function denoted by or (where the argument x is written as an exponent). Unless otherwise specified, the term generally refers to the positive-valued functio

Soboleva modified hyperbolic tangent

The Soboleva modified hyperbolic tangent, also known as (parametric) Soboleva modified hyperbolic tangent activation function ([P]SMHTAF), is a special S-shaped function based on the hyperbolic tangen

Square (algebra)

In mathematics, a square is the result of multiplying a number by itself. The verb "to square" is used to denote this operation. Squaring is the same as raising to the power 2, and is denoted by a sup

Turán's method

In mathematics, Turán's method provides lower bounds for exponential sums and complex power sums. The method has been applied to problems in equidistribution. The method applies to sums of the form wh

Stretched exponential function

The stretched exponential function is obtained by inserting a fractional power law into the exponential function.In most applications, it is meaningful only for arguments t between 0 and +∞. With β =

Logarithmic spiral

A logarithmic spiral, equiangular spiral, or growth spiral is a self-similar spiral curve that often appears in nature. The first to describe a logarithmic spiral was Albrecht Dürer (1525) who called

Gudermannian function

In mathematics, the Gudermannian function relates a hyperbolic angle measure to a circular angle measure called the gudermannian of and denoted . The Gudermannian function reveals a close relationship

Gaussian function

In mathematics, a Gaussian function, often simply referred to as a Gaussian, is a function of the base form and with parametric extensionfor arbitrary real constants a, b and non-zero c. It is named a

Addition-chain exponentiation

In mathematics and computer science, optimal addition-chain exponentiation is a method of exponentiation by a positive integer power that requires a minimal number of multiplications. Using the form o

Infra-exponential

A growth rate is said to be infra-exponential or subexponential if it is dominated by all exponential growth rates, however great the doubling time. A continuous function with infra-exponential growth

Euler's identity

In mathematics, Euler's identity (also known as Euler's equation) is the equality where e is Euler's number, the base of natural logarithms,i is the imaginary unit, which by definition satisfies i2 =

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: Lindemann–Weierstrass theorem

Wheat and chessboard problem

The wheat and chessboard problem (sometimes expressed in terms of rice grains) is a mathematical problem expressed in textual form as: If a chessboard were to have wheat placed upon each square such t

Double exponential function

A double exponential function is a constant raised to the power of an exponential function. The general formula is (where a>1 and b>1), which grows much more quickly than an exponential function. For

Base (exponentiation)

In exponentiation, the base is the number b in an expression of the form bn.

Baker–Campbell–Hausdorff formula

In mathematics, the Baker–Campbell–Hausdorff formula is the solution for to the equation for possibly noncommutative X and Y in the Lie algebra of a Lie group. There are various ways of writing the fo

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 (u

Power law

In statistics, a power law is a functional relationship between two quantities, where a relative change in one quantity results in a proportional relative change in the other quantity, independent of

Catenary

In physics and geometry, a catenary (US: /ˈkætənɛri/, UK: /kəˈtiːnəri/) is the curve that an idealized hanging chain or cable assumes under its own weight when supported only at its ends in a uniform

Transseries

In mathematics, the field of logarithmic-exponential transseries is a non-Archimedean ordered differential field which extends comparability of asymptotic growth rates of elementary nontrigonometric f

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.

Common antilogarithm

No description available.

Pentation

In mathematics, pentation (or hyper-5) is the next hyperoperation after tetration and before hexation. It is defined as iterated (repeated) tetration, just as tetration is iterated exponentiation. It

Prime power

In mathematics, a prime power is a positive integer which is a power of a single prime number.For example: 7 = 71, 9 = 32 and 64 = 26 are prime powers, while6 = 2 × 3, 12 = 22 × 3 and 36 = 62 = 22 × 3

Natural exponential family

In probability and statistics, a natural exponential family (NEF) is a class of probability distributions that is a special case of an exponential family (EF).

P-adic exponential function

In mathematics, particularly p-adic analysis, the p-adic exponential function is a p-adic analogue of the usual exponential function on the complex numbers. As in the complex case, it has an inverse f

Ordered exponential field

In mathematics, an ordered exponential field is an ordered field together with a function which generalises the idea of exponential functions on the ordered field of real numbers.

Decadic antilogarithm

No description available.

Exponential tree

An exponential tree is almost identical to a binary search tree, with the exception that the dimension of the tree is not the same at all levels. In a normal binary search tree, each node has a dimens

Volatility tax

The volatility tax is a mathematical finance term, formalized by hedge fund manager Mark Spitznagel, describing the effect of large investment losses (or volatility) on compound returns. It has also b

Exponentiation by squaring

In mathematics and computer programming, exponentiating by squaring is a general method for fast computation of large positive integer powers of a number, or more generally of an element of a semigrou

Proof that e is irrational

The number e was introduced by Jacob Bernoulli in 1683. More than half a century later, Euler, who had been a student of Jacob's younger brother Johann, proved that e is irrational; that is, that it c

Natural antilogarithm

No description available.

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 ma

Softmax function

The softmax function, also known as softargmax or normalized exponential function, converts a vector of K real numbers into a probability distribution of K possible outcomes. It is a generalization of

Compound interest

Compound interest is the addition of interest to the principal sum of a loan or deposit, or in other words, interest on principal plus interest. It is the result of reinvesting interest, or adding it

Hyperbolic functions

In mathematics, hyperbolic functions are analogues of the ordinary trigonometric functions, but defined using the hyperbola rather than the circle. Just as the points (cos t, sin t) form a circle with

Zero to the power of zero

Zero to the power of zero, denoted by 00, is a mathematical expression that is either defined as 1 or left undefined, depending on context. In algebra and combinatorics, one typically defines 00 = 1.

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,

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