Transformation formulae for multivariable basic hypergeometric series

T. H. Baker; P. J. Forrester

Transformation formulae for multivariable basic hypergeometric series

Quantum Algebra 2007-05-23 v1 Classical Analysis and ODEs

Authors: 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 ${}_2\phi_1$ transformation, the $q$ -Pfaff-Kummer and Euler transformations, the $q$ -Saalsch\"utz summation formula and Sear's transformation for terminating, balanced ${}_4\phi_3$ series. For bilateral series, we rederive Kaneko's analogue of the ${}_1\psi_1$ summation formula and give multivariable extensions of Bailey's ${}_2\psi_2$ transformations.

Keywords

hypergeometric functions macdonald polynomials exponential sums

Cite

@article{arxiv.math/9803146,
  title  = {Transformation formulae for multivariable basic hypergeometric series},
  author = {T. H. Baker and P. J. Forrester},
  journal= {arXiv preprint arXiv:math/9803146},
  year   = {2007}
}

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Latex2e, 17 pages

Transformation formulae for multivariable basic hypergeometric series

Abstract

Keywords

Cite

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