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A synonym for analytic function, regular function, differentiable function, complex differentiable function, and holomorphic map (Krantz 1999, p. 16). The word derives from ...

A generalization of the Euler L-function associated with a Grössencharakter.

The (complete) gamma function Gamma(n) is defined to be an extension of the factorial to complex and real number arguments. It is related to the factorial by Gamma(n)=(n-1)!, ...

The sawtooth wave, called the "castle rim function" by Trott (2004, p. 228), is the periodic function given by S(x)=Afrac(x/T+phi), (1) where frac(x) is the fractional part ...

The Mittag-Leffler function (Mittag-Leffler 1903, 1905) is an entire function defined by the series E_alpha(z)=sum_(k=0)^infty(z^k)/(Gamma(alphak+1)) (1) for alpha>0. It is ...

An apodization function (also called a tapering function or window function) is a function used to smoothly bring a sampled signal down to zero at the edges of the sampled ...

An Artin L-function over the rationals Q encodes in a generating function information about how an irreducible monic polynomial over Z factors when reduced modulo each prime. ...

A solution to the spherical Bessel differential equation. The two types of solutions are denoted j_n(x) (spherical Bessel function of the first kind) or n_n(x) (spherical ...

If a complex function is analytic at all finite points of the complex plane C, then it is said to be entire, sometimes also called "integral" (Knopp 1996, p. 112). Any ...

A function f(x) is said to be periodic (or, when emphasizing the presence of a single period instead of multiple periods, singly periodic) with period p if f(x)=f(x+np) for ...