Well-posed reduction formulas for the $q$-Kampé-de-Fériet function

Abstract

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.