Transformation formulae for multivariable basic hypergeometric series
arXiv:math/9803146
Abstract
We study multivariable (bilateral) basic hypergeometric series associated with (type ) Macdonald polynomials. We derive several transformation and summation properties for such series including analogues of Heine's transformation, the -Pfaff-Kummer and Euler transformations, the -Saalschütz summation formula and Sear's transformation for terminating, balanced series. For bilateral series, we rederive Kaneko's analogue of the summation formula and give multivariable extensions of Bailey's transformations.
Latex2e, 17 pages