Multilateral transformations of q-series with quotients of parameters that are nonnegative integer powers of q

Details Multilateral transformations of q-series with quotients of parameters that are nonnegative integer powers of q Multilateral transformations of q-series with quotients of parameters that are nonnegative integer powers of q

2001-02-21

arxiv.org/abs/math/0102174v1

Contemp. Math. 291 (2001), 203-227

Mathematics

Classical Analysis and ODEs

Scientific paper

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)).

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