Summations and transformations for multiple basic and elliptic hypergeometric series by determinant evaluations

Abstract

Using multiple q-integrals and a determinant evaluation, we establish a multivariable extension of Bailey's nonterminating 10-phi-9 transformation. From this result, we deduce new multivariable terminating 10-phi-9 transformations, 8-phi-7 summations and other identities. We also use similar methods to derive new multivariable 1-psi-1 summations. Some of our results are extended to the case of elliptic hypergeometric series.

29 pages, minor changes; to appear in Indag. Math., special volume dedicated to Tom Koornwinder

References in corpus (2)

• Summation and transformation formulas for elliptic hypergeometric series
• A nonterminating 8-phi-7 summation for the root system C_r

Cited by in corpus (18)

• Essays on the theory of elliptic hypergeometric functions
• Elliptic enumeration of nonintersecting lattice paths
• Elliptic hypergeometric functions associated with root systems
• Special polynomials related to the supersymmetric eight-vertex model. I. Behaviour at cusps
• Gustafson-Rakha-Type Elliptic Hypergeometric Series
• Multilateral basic hypergeometric summation identities and hyperoctahedral group symmetries
• Multiple basic hypergeometric transformation formulas arising from the balanced duality transformation
• New transformations for elliptic hypergeometric series on the root system An
• An elliptic determinant transformation
• Extensions of the well-poised and elliptic well-poised Bailey lemma
• A duality formula between elliptic determinants
• An Elliptic $B{C}_n$ Bailey Lemma, Multiple Rogers--Ramanujan Identities and Euler's Pentagonal Number Theorems
• Schur Q-polynomials, multiple hypergeometric series and enumeration of marked shifted tableaux
• A multilateral Bailey Lemma and multiple Andrews--Gordon identities
• Multiple analogues of binomial coefficients and related families of special numbers
• General Multi-sum Transformations and Some Implications
• Advanced Determinant Calculus: A Complement
• Summation formulae for elliptic hypergeometric series