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There are (at least) three types of Euler transforms (or transformations). The first is a set of transformations of hypergeometric functions, called Euler's hypergeometric ...

Gossiping and broadcasting are two problems of information dissemination described for a group of individuals connected by a communication network. In gossiping, every person ...

Keller conjectured that tiling an n-dimensional space with n-dimensional hypercubes of equal size yields an arrangement in which at least two hypercubes have an entire ...

The difference between the measured or inferred value of a quantity x_0 and its actual value x, given by Deltax=x_0-x (sometimes with the absolute value taken) is called the ...

Functions which can be expressed in terms of Legendre functions of the first and second kinds. See Abramowitz and Stegun (1972, p. 337). P_(-1/2+ip)(costheta) = (1) = ...

A hypergeometric function in which one parameter changes by +1 or -1 is said to be contiguous. There are 26 functions contiguous to _2F_1(a,b;c;x) taking one pair at a time. ...

Series expansions of the parabolic cylinder functions U(a,x) and W(a,x). The formulas can be found in Abramowitz and Stegun (1972).

Given a Jacobi amplitude phi in an elliptic integral, the argument u is defined by the relation phi=am(u,k). It is related to the elliptic integral of the first kind F(u,k) ...

A parameter n used to specify an elliptic integral of the third kind Pi(n;phi,k).

The exsecant is a little-used trigonometric function defined by exsec(x)=secx-1, (1) where secx is the secant. The exsecant can be extended to the complex plane as ...