Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Expansion Formulas of Basic Hypergeometric Series via the
  (1-xy,y-x)--Inversion and Its Applications   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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The categories of this paper are: cs
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The categories of this paper are: physics
32
The categories of this paper are: atom-ph
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The categories of this paper are: cmp-lg
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The categories of this paper are: astro-ph
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The categories of this paper are: nucl-th
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The categories of this paper are: bayes-an
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The categories of this paper are: q-bio
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The categories of this paper are: funct-an
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The categories of this paper are: stat
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The categories of this paper are: nucl-ex
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The categories of this paper are: patt-sol
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The categories of this paper are: hep-ph
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The categories of this paper are: math-ph
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The categories of this paper are: econ
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The categories of this paper are: comp-gas