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An asymmetrical apodization function defined by M(x,b,d)={0 for x<-b; (x-b)/(2b) for -b<x<b; 1 for b<x<b+2d; 0 for x<b+2d, (1) where the two-sided portion is 2b long (total) ...

If Li_2(x) denotes the usual dilogarithm, then there are two variants that are normalized slightly differently, both called the Rogers L-function (Rogers 1907). Bytsko (1999) ...

The Coulomb wave function is a special case of the confluent hypergeometric function of the first kind. It gives the solution to the radial Schrödinger equation in the ...

Given a finitely generated Z-graded module M over a graded ring R (finitely generated over R_0, which is an Artinian local ring), the Hilbert function of M is the map ...

Define S_n(x) = sum_(k=1)^(infty)(sin(kx))/(k^n) (1) C_n(x) = sum_(k=1)^(infty)(cos(kx))/(k^n), (2) then the Clausen functions are defined by ...

The regularized gamma functions are defined by P(a,z) = (gamma(a,z))/(Gamma(a)) (1) Q(a,z) = (Gamma(a,z))/(Gamma(a)), (2) where gamma(a,z) and Gamma(a,z) are incomplete gamma ...

There are several functions called "Lommel functions." One type of Lommel function appear in the solution to the Lommel differential equation and are given by ...

A function f(x) is logarithmically convex on the interval [a,b] if f>0 and lnf(x) is convex on [a,b]. If f(x) and g(x) are logarithmically convex on the interval [a,b], then ...

A function f(z) is said to be doubly periodic if it has two periods omega_1 and omega_2 whose ratio omega_2/omega_1 is not real. A doubly periodic function that is analytic ...

The central beta function is defined by beta(p)=B(p,p), (1) where B(p,q) is the beta function. It satisfies the identities beta(p) = 2^(1-2p)B(p,1/2) (2) = ...