Ramanujan-type formulae for \(1/\pi: q\)-analogues. (English) Zbl 1436.11024

Summary: The hypergeometric formulae designed by Ramanujan more than a century ago for efficient approximation of \(\pi\), Archimedes’ constant, remain an attractive object of arithmetic study. In this note we discuss some \(q\)-analogues of Ramanujan-type evaluations and of related supercongruences.


11B65 Binomial coefficients; factorials; \(q\)-identities
11Y60 Evaluation of number-theoretic constants
33C20 Generalized hypergeometric series, \({}_pF_q\)
33D15 Basic hypergeometric functions in one variable, \({}_r\phi_s\)
Full Text: DOI arXiv


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