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WZ pairs and \(q\)-analogues of Ramanujan series for \(1/\pi\). (English) Zbl 1405.11021
Summary: We prove \(q\)-analogues of two Ramanujan-type series for \(1/\pi\) from \(q\)-analogues of ordinary WZ pairs.

11B65 Binomial coefficients; factorials; \(q\)-identities
33C20 Generalized hypergeometric series, \({}_pF_q\)
33F10 Symbolic computation of special functions (Gosper and Zeilberger algorithms, etc.)
33D15 Basic hypergeometric functions in one variable, \({}_r\phi_s\)
Full Text: DOI
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