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Expansion Formulas of Basic Hypergeometr...
Wang, Jin...

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Expansion Formulas of Basic Hypergeometric Series via the (1-xy,y-x)--Inversion and Its Applications by Wang, Jin ( Author )
Lemonjar Open Access
Australian National University
01-08-2023
With the use of the $(f,g)$-matrix inversion under specializations that $f=1-xy,g=y-x$, we establish an $(1-xy,y-x)$-expansion formula. When specialized to basic hypergeometric series, this $(1-xy,y-x)$-expansion formula leads us to some expansion formulas expressing any ${}_{r}\phi_{s}$ series in variable $x~t$ in terms of a linear combination of ${}_{r+2}\phi_{s+1}$ series in $t$, as well as various specifications. All these results can be regarded as common generalizations of many konwn expansion formulas in the setting of $q$-series. As specific 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 ${}_1\psi_1$ summation formula, as well as a transformation for certain well-poised Bailey pairs, are presented.
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English
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MYR 0.01
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http://arxiv.org/abs/1301.3582
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