$q$-Analogues of two product formulas of hypergeometric functions by Bailey
Michael J. Schlosser
TL;DR
This paper derives new $q$-analogues of product formulas for hypergeometric functions using Andrews' summation theorems, extending Bailey's classical results with novel proofs and formulas.
Contribution
It introduces two new $q$-analogues of hypergeometric product formulas, expanding the mathematical understanding of basic hypergeometric functions.
Findings
Derived two $q$-analogues of hypergeometric product formulas
Extended Bailey's classical formulas using Andrews' summation theorems
Provided alternative proofs for existing formulas
Abstract
We use Andrews' -analogues of Watson's and Whipple's summation theorems to deduce two formulas for products of specific basic hypergeometric functions. These constitute -analogues of corresponding product formulas for ordinary hypergeometric functions given by Bailey. The first formula was obtained earlier by Jain and Srivastava by a different method.
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