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Hypergeometric modular equations. (English) Zbl 1428.33014
Summary: We record \(\binom{42}{2}+\binom{23}{2}+\binom{13}{2}=1192\) functional identities that, apart from being amazingly amusing in themselves, find application in the derivation of Ramanujan-type formulas for \(1/ \pi\) and in the computation of mathematical constants.

MSC:
33C20 Generalized hypergeometric series, \({}_pF_q\)
11B65 Binomial coefficients; factorials; \(q\)-identities
11F11 Holomorphic modular forms of integral weight
11Y60 Evaluation of number-theoretic constants
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