U(n) very-well-poised 10Ø9 transformations

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.

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 ...

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...

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