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A generalization of the hypergeometric function identity (1) to the generalized hypergeometric function _3F_2(a,b,c;d,e;x). Darling's products are (2) and (3) which reduce to ...

The Dürer graph is the skeleton of Dürer's solid, which is the generalized Petersen graph GP(6,2). It is illustrated above in a number of embeddings. It is implemented in the ...

sum_(n=0)^(infty)(-1)^n[((2n-1)!!)/((2n)!!)]^3 = 1-(1/2)^3+((1·3)/(2·4))^3+... (1) = _3F_2(1/2,1/2,1/2; 1,1;-1) (2) = [_2F_1(1/4,1/4; 1;-1)]^2 (3) = ...

The singular support of a generalized function u is the complement of the largest open set on which u is smooth. Roughly speaking, it is the closed set where the distribution ...

Slater (1960, p. 31) terms the identity _4F_3[a,1+1/2a,b,-n; 1/2a,1+a-b;1+a+n]=((1+a)_n(1/2+1/2a-b)_n)/((1/2+1/2a)_n(1+a-b)_n) for n a nonnegative integer the "_4F_3[1] ...

"The" I graph is the path graph on two vertices: P_2. An I-graph I(n,j,k) for 1<=j,k<n and j,k!=n/2 is a generalization of a generalized Petersen graph and has vertex set ...

Whipple derived a great many identities for generalized hypergeometric functions, many of which are consequently known as Whipple's identities (transformations, etc.). Among ...

The constant pi, denoted pi, is a real number defined as the ratio of a circle's circumference C to its diameter d=2r, pi = C/d (1) = C/(2r) (2) pi has decimal expansion ...

The algorithm of constructing and interpreting a quotient-difference table which allows interconversion of continued fractions, power series, and rational functions ...

First published in Riemann's groundbreaking 1859 paper (Riemann 1859), the Riemann hypothesis is a deep mathematical conjecture which states that the nontrivial Riemann zeta ...