the exponential function is the unique real function which maps zero to one and has a derivative everywhere equal to its value. The exponential of a...

Exponential growth occurs when a quantity grows as an exponential function of time. The quantity grows at a rate directly proportional to its present size...

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...

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...

tetration in Wiktionary, the free dictionary. Ackermann function Big O notation Double exponential function Hyperoperation Iterated logarithm Symmetric level-index...

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

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

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...

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

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....

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...

approximately equal to 2.71828 that is the base of the natural logarithm and exponential function. It is sometimes called Euler's number, after the Swiss mathematician...

integer Mathematics portal Double exponential function – Exponential function of an exponential function Exponential decay – Decrease in value at a rate...

With hyperbolic angle u, the hyperbolic functions sinh and cosh can defined with the exponential function eu. In the figure A = ( e − u , e u ) ,  ...

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

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

{\displaystyle L} . The exponential function with negated argument ( e − x {\displaystyle e^{-x}} ) is used to define the standard logistic function, depicted at...

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...

trigonometric, hyperbolic, and exponential functions, and their inverses (e.g., arcsin, log, or x1/n). All elementary functions are continuous on their domains...

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

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...

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...

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

complex functions are defined in this way, including the complex exponential function, complex logarithm functions, and trigonometric functions. Complex...

are various types of generating functions, including ordinary generating functions, exponential generating functions, Lambert series, Bell series, and...

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

algebraic function. Examples of transcendental functions include the exponential function, the logarithm function, the hyperbolic functions, and the trigonometric...

the rate (i.e. back off). The rate reduction can be modelled as an exponential function: t = b c {\displaystyle t=b^{c}} or f = 1 b c {\displaystyle f={\frac...

the exponential map is one of the primary reasons that Lie algebras are a useful tool for studying Lie groups. The ordinary exponential function of mathematical...

types of functions Elementary functions are functions built from basic operations (e.g. addition, exponentials, logarithms...) Algebraic functions are functions...