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Transformation formulae for multivariable basic hypergeometric series

T. H. Baker·P. J. Forrester
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Abstract

We study multivariable (bilateral) basic hypergeometric series associated with (type $A$) Macdonald polynomials. We derive several transformation and summation properties for such series including analogues of Heine's ${}_2ϕ_1$ transformation, the $q$-Pfaff-Kummer and Euler transformations, the $q$-Saalschütz summation formula and Sear's transformation for terminating, balanced ${}_4ϕ_3$ series. For bilateral series, we rederive Kaneko's analogue of the ${}_1ψ_1$ summation formula and give multivariable extensions of Bailey's ${}_2ψ_2$ transformations.

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T. H. Baker, P. J. Forrester. 1998-03-30. Transformation formulae for multivariable basic hypergeometric series. https://arxiv.org/abs/math/9803146

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