Summation identities and transformations for hypergeometric series

Summation Formulae for Noncommutative Hypergeometric Series

Hypergeometric series with noncommutative parameters and argument, in the special case involving square matrices, have recently been studied by a number of researchers including (in alphabetical order) Durán, Duval, Grünbaum, Iliev, Ovsienko, Pacharoni, Tirao, and others. See [3, 6, 8, 9, 10, 11, 12, 16] for some selected papers. The subject of hypergeometric series involving matrices is closel...

qMultiSum--a package for proving q-hypergeometric multiple summation identities

A Mathematica package for finding recurrences for q-hypergeometric multiple sums is introduced. Together with a detailed description of the theoretical background, we present several examples to illustrate its usage and range of applicability. In particular, various computer proofs of recently discovered identities are exhibited.

SUMMATION IDENTITIES AND SPECIAL VALUES OF HYPERGEOMETRIC SERIES IN THE p-ADIC SETTING

We prove hypergeometric type summation identities for a function defined in terms of quotients of the p-adic gamma function by counting points on certain families of hyperelliptic curves over Fq . We also find certain special values of that function.

87. Binomial Coefficient Identities and Hypergeometric Series

In recent months I have come across many instances in which someone has found what they believe is a new result, in which they evaluate in closed form a sum involving binomial coefficients or factorials. In each case they have managed to do that either by using the recent powerful method of Wilf and Zeilberger (the W–Z method) [6], or by comparing coefficients in some ad hoc algebraic identity....

Summation theorems for multidimensional basic hypergeometric series by determinant evaluations