The very well poised $\sb{6}\psi \sb{6}$. II

Orthogonality of Very Well-poised Series

Rodrigues formulas for very well-poised basic hypergeometric series of any order are given. Orthogonality relations are found for rational functions which generalize Rahman’s 10φ9 biorthogonal rational functions. A pair of orthogonal rational functions of type RII is identified. Elliptic analogues of some of these results are also included.

Some Remarks on Very - Well - Poised 8 φ 7 Series

Nonpolynomial basic hypergeometric eigenfunctions of the Askey–Wilson second order difference operator are known to be expressible as very-well-poised 8φ7 series. In this paper we use this fact to derive various basic hypergeometric and theta function identities. We relate most of them to identities from the existing literature on basic hypergeometric series. This leads for example to a new der...

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

A simple proof of Bailey’s very-well-poised 6ψ6 summation

Using Rogers’ nonterminating 6φ5 summation and elementary series manipulations, we give a simple proof of Bailey’s very-well-poised 6ψ6 summation. This proof extends M. Jackson’s first proof of Ramanujan’s 1ψ1 summation.

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...