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...

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...

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...

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

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

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

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

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...

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....

Mathematics portal Double exponential function Exponential decay Exponential field Exponential growth Pentation List of exponential topics Modular exponentiation...

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

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

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...

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

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...

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

model theory, Tarski's exponential function problem asks whether the theory of the real numbers together with the exponential function is decidable. Alfred...

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...

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

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

failures is approximated using the exponential function, then the exponential curve gives the probability density function, fT, for AC failure times. Another...

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

algebraic function is the same, with nth roots and roots of polynomials also allowed. An elementary function is the same, with logarithms and exponential functions...

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

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

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

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...