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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.

##### MSC:
 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, $${}_r\phi_s$$
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##### References:
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