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An extension of the Ramanujan-Bailey formula. (Une extension d’une formule de Ramanujan-Bailey.) (French. English summary) Zbl 0980.33500

Summary: The Ramanujan-Bailey identity that establishes a symmetric relation between two hypergeometric series \({}_3F_2\) is extended to a symmetric relation between two hypergeometric series \({}_4F_3\). We also give a symmetric model that makes this symmetry evident. Finally, we obtain a \(q\)-analog of this extension.

MSC:

33C20 Generalized hypergeometric series, \({}_pF_q\)
05A19 Combinatorial identities, bijective combinatorics
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