Summations and transformations for very well-poised hypergeometric functions 2q+5F2q+4(1) and 2q+7F2q+6(1) with arbitrary integral parameter differences

Multiple-integral Representations of Very-well-poised Hypergeometric Series

Transformations of well-poised hypergeometric functions over finite fields

We define a hypergeometric function over finite fields which is an analogue of the classical generalized hypergeometric series. We prove that this function satisfies many transformation and summation formulas. Some of these results are analogous to those given by Dixon, Kummer and Whipple for the well-poised classical series. We also discuss this function’s relationship to other finite field an...

Well-poised Hypergeometric Transformations of Euler-type Multiple Integrals

Several new multiple-integral representations are proved for well-poised hypergeometric series and integrals. The results yield, in particular, transformations of the multiple integrals that cannot be achieved by evident changes of variable. All this generalizes some classical results of Whipple and Bailey in analysis and, on the other hand, certain analytic constructions with known connection ...

Integral Properties of Zonal Spherical Functions, Hypergeometric Functions and Invariant

Some integral properties of zonal spherical functions, hypergeometric functions and invariant polynomials are studied for real normed division algebras.

An Identity of Andrews, Multiple Integrals, and Very-well-poised Hypergeometric Series

Abstract. We give a new proof of a theorem of Zudilin that equates a very-well-poised hypergeometric series and a particular multiple integral. This integral generalizes integrals of Vasilenko and Vasilyev which were proposed as tools in the study of the arithmetic behaviour of values of the Riemann zeta function at integers. Our proof is based on limiting cases of a basic hypergeometric identi...