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Transformations and Summations for Bilateral Basic Hypergeometric Series
Howard S Cohl1, Michael J Schlosser2
1Applied and Computational Mathematics Division, National Institute of Standards and Technology, Mission Viejo, 92694 CA, USA.
Abstract:
We review and derive transformation and summation formulas for bilateral basic hypergeometric series. Our study focuses on consequences of certain bilateral extensions of two important results by Bailey, namely a transformation for very-well-poised series in terms of two balanced series, and a transformation connecting three series. Two rather recently discovered transformations of bilateral basic very-well-poised , one by Zhang and Zhang, the other by Wei and Yu, serve as the starting point of our investigations. From these transformations we work out interesting special cases that were not considered before, including explicit bilateral quadratic and cubic summations. We further explicitly record noteworthy lower-level transformations derived by taking suitable limits and deduce more transformations by exploiting the symmetry of the parameters in the series.
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