WZ pairs and \(q\)-analogues of Ramanujan series for \(1/\pi\). (English) Zbl 1405.11021

Guillera, Jesús

J. Difference Equ. Appl. 24, No. 12, 1871-1879 (2018).

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

MSC:

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, \({}_r\phi_s\)

Keywords:

hypergeometric series; WZ and \(q\)-WZ pairs; \(q\)-identities; supercongruences

References:

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