Well-posed reduction formulas for the q-Kampé-de-Fériet function
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By using the limiting case of Watson’s q-Whipple transformation as n → ∞, we investigate the transformations of the nonterminating q-Kampé-de-Fériet series. Further, new formulas for the transformations and well-posed reduction formulas are established for the basic Clausen hypergeometric series. Several remarkable formulas are also found for new function classes beyond the q-Kampé-de-Fériet function.
KeywordsHypergeometric Series Transformation Formula Double Series Reduction Formula Basic Hypergeometric Series