Transformation formulae for multivariable basic hypergeometric series
Baker, T. H. · Forrester, P. J.
Original · EN
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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