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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...

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...

formula in complex analysis that establishes the fundamental relationship between the trigonometric functions and the complex exponential function. Euler's...

{\displaystyle e^{x+iy}=(\cosh x+\sinh x)(\cos y+i\sin y)} for the general complex exponential function. Additionally, e x = 1 + tanh ⁡ x 1 − tanh ⁡ x = 1 + tanh...

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

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

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

} from the real numbers to any complex argument z. This extended exponential function still satisfies the exponential identity, and is commonly used for...

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

are not zero, then function S has multitudes of additional singularities and cutlines in the complex plane, due to the exponential growth of sin and cos...

entire function. In fact, the gamma function corresponds to the Mellin transform of the negative exponential function: Γ ( z ) = M { e − x } ( z ) . {\displaystyle...

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...

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

In mathematics, a holomorphic function is a complex-valued function of one or more complex variables that is complex differentiable in a neighbourhood...

x is an odd function, so erf x = −erf(−x). Exponential bounds and a pure exponential approximation for the complementary error function are given by...

half of the complex plane). A discrete-time input-to-output LTI system is exponentially stable if and only if the poles of its transfer function lie strictly...

{5}{8}}}}}}\ldots } The exponential function can be extended to a function which gives a complex number as ez for any arbitrary complex number z; simply use...

converse relation of the function f(w) = wew, where w is any complex number and ew is the exponential function. The function is named after Johann Lambert...

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...