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- W1945993213 abstract "With the use of the $(f,g)$-inversion formula under specializations that $f=1-xy,g=y-x$, we establish an expansion of (modified) basic hypergeometric ${}_{r}phi_{s}$ series in variable $x~t$ as a linear combination of ${}_{r+2}phi_{s+1}$ series in $t$ and its various specifications. These expansions can be regarded as common generalizations of Carlitz's, Liu's, and Chu's expansion in the setting of $q$-series. As direct applications, some new transformation formulas of $q$-series including new approach to the Askey-Wilson polynomials, the Rogers-Fine identity, Andrews' four-parametric reciprocity theorem and Ramanujan's ${}_1psi_1$ summation formula, as well as a transformation for certain well-poised Bailey pairs, are presented." @default.
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- W1945993213 date "2013-01-16" @default.
- W1945993213 modified "2023-09-27" @default.
- W1945993213 title "An Expansion Formula of Basic Hypergeometric Series via the (1-xy,y-x)--Inversion and Its Applications" @default.
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