Transformation formulae for multivariable basic hypergeometric series
T. H. Baker, P. J. Forrester
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 2ϕ1 transformation, the q-Pfaff-Kummer and Euler transformations, the q-Saalschütz summation formula and Sear's transformation for terminating, balanced 4ϕ3 series. For bilateral series, we rederive Kaneko's analogue of the 1ψ1 summation formula and give multivariable extensions of Bailey's 2ψ2 transformations.
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