Multilateral transformations of qseries with quotients of parameters that are nonnegative integer powers of q
Abstract
We give multidimensional generalizations of several transformation formulae for basic hypergeometric series of a specific type. Most of the upper parameters of the series differ multiplicatively from corresponding lower parameters by a nonnegative integer power of the base q. In one dimension, formulae for such series have been found, in the q > 1 case, by B. M. Minton and P. W. Karlsson, and in the basic case by G. Gasper, by W. C. Chu, and more recently by the author. Our identities involve multilateral basic hypergeometric series associated to the root system A_r (or equivalently, the unitary group U(r+1)).
 Publication:

arXiv Mathematics eprints
 Pub Date:
 February 2001
 arXiv:
 arXiv:math/0102174
 Bibcode:
 2001math......2174S
 Keywords:

 Mathematics  Classical Analysis and ODEs;
 Mathematics  Combinatorics;
 Mathematics  Quantum Algebra;
 33D15;
 33D67
 EPrint:
 Contemp. Math. 291 (2001), 203227