Michael J. Schlosser
Multilateral transformations of q-series with quotients of
parameters that are nonnegative integral powers of q
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 Ar (or equivalently, the unitary group
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