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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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