The exponential function is a mathematical function denoted by f ( x ) = exp ⁡ ( x ) {\displaystyle f(x)=\exp(x)} or e x {\displaystyle e^{x}} (where...

The stretched exponential function f β ( t ) = e − t β {\displaystyle f_{\beta }(t)=e^{-t^{\beta }}} is obtained by inserting a fractional power law into...

A double exponential function is a constant raised to the power of an exponential function. The general formula is f ( x ) = a b x = a ( b x ) {\displaystyle...

the quantity itself. Described as a function, a quantity undergoing exponential growth is an exponential function of time, that is, the variable representing...

In mathematics, the exponential function can be characterized in many ways. This article presents some common characterizations, discusses why each makes...

In mathematics, a half-exponential function is a functional square root of an exponential function. That is, a function f {\displaystyle f} such that f...

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...

The softmax function, also known as softargmax: 184  or normalized exponential function,: 198  converts a vector of K real numbers into a probability...

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...

exponential functions. For a complete list of integral functions, please see the list of integrals. Indefinite integrals are antiderivative functions...

Commons has media related to tetration. Ackermann function Big O notation Double exponential function Hyperoperation Iterated logarithm Symmetric level-index...

computation of compound interest. It is the value at 1 of the (natural) exponential function, commonly denoted e x . {\displaystyle e^{x}.} It is also the sum...

gamma, and Poisson distributions. The probability density function (pdf) of an exponential distribution is f ( x ; λ ) = { λ e − λ x x ≥ 0 , 0 x < 0....

window function. Whereas in the simple moving average the past observations are weighted equally, exponential functions are used to assign exponentially decreasing...

single-parameter exponential family is a set of probability distributions whose probability density function (or probability mass function, for the case...

define the hyperbolic functions. In terms of the exponential function: Hyperbolic sine: the odd part of the exponential function, that is, sinh ⁡ x = e...

to be a multi-valued function. For example, the complex logarithm is the multi-valued inverse of the complex exponential function. Similarly, the discrete...

transcendental functions include the exponential function, the logarithm, and the trigonometric functions. Formally, an analytic function f (z) of one real or complex...

In mathematics, the matrix exponential is a matrix function on square matrices analogous to the ordinary exponential function. It is used to solve systems...

real-valued function of a positive real variable, is the inverse function of the exponential function, leading to the identities: e ln ⁡ x = x  if  x ∈ R + ln...

fundamental relationship between the trigonometric functions and the complex exponential function. Euler's formula states that, for any real number x...

failures is approximated using the exponential function, then the exponential curve gives the probability density function, f(t), for air conditioner failure...

to exponentiation, including: Exponential function, also: Matrix exponential, the matrix analogue to the above Exponential decay, decrease at a rate proportional...

all x. The exponential generating function of the Bell numbers is the exponential function of the predecessor of the exponential function: exp ⁡ ( exp...

an exponential sum may be a finite Fourier series (i.e. a trigonometric polynomial), or other finite sum formed using the exponential function, usually...

portal Double exponential function Exponential decay Exponential field Exponential growth Hyperoperation Tetration Pentation List of exponential topics Modular...

the nature of the exponential function e − x {\displaystyle e^{-x}} , it is often sufficient to compute the standard logistic function for x {\displaystyle...

to the same number by the exponential function. This means that the exponential function does not have an inverse function in the standard sense. There...

one of the most important examples of a power series, as are the exponential function formula e x = ∑ n = 0 ∞ x n n ! = 1 + x + x 2 2 ! + x 3 3 ! + ⋯ ...

sin and cos can be defined for all complex numbers in terms of the exponential function, via power series, or as solutions to differential equations given...