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Some identities between basic hypergeometric series deriving from a new Bailey-type transformation. (English) Zbl 1147.33002

For a (WP-)Bailey pair \(\alpha_n(a,b),\beta_n(a,b)\), where \(n=0,1,2,\dots\), that is, for two sequences satisfying \[ \beta_n=\sum_{k=0}^n\frac{(b/a;q)_{n-k}(b;q)_{n+k}} {(q;q)_{n-k}(aq;q)_{n+k}}\alpha_k, \qquad (x;q)_n:=\prod_{k=0}^{n-1}(1-xq^k), \] under suitable convergence conditions the authors derive a 3-line transformation formula. The result is illustrated by eight corollaries which provide transformations of generalized hypergeometric series.

MSC:

33D15 Basic hypergeometric functions in one variable, \({}_r\phi_s\)
33C20 Generalized hypergeometric series, \({}_pF_q\)
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