Gaurav Bhatnagar and Michael J. Schlosser
In this paper, we derive multivariable generalizations of Bailey's
classical terminating balanced very-well-poised
We work in the setting of multiple basic hypergeometric series
very-well-poised on the root systems An,
Cn, and Dn.
Following the distillation of Bailey's ideas by Gasper and Rahman,
we use a suitable interchange of multisums.
We obtain Cn and Dn
transformations from an interchange of multisums, combined with
An, Cn, and Dn
extensions of Jackson's 8φ7 summation.
Milne and Newcomb have previously obtained an analogous formula for
Special cases of our 10φ9 transformations
include several new multivariable generalizations of Watson's transformation
of an 8φ7 into a multiple of a
4φ3 series. We also deduce
multidimensional extensions of Sears'
the second iterate of Heine's transformation, the q-Gauss summation
theorem, and of the q-binomial theorem.
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