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Domb’s numbers and Ramanujan-Sato type series for \(1/\pi\). (English) Zbl 1122.11087

Summary: We construct a general series for \(\frac{1}{\pi}\). We indicate that Ramanujan’s \(\frac{1}{\pi}\)-series are all special cases of this general series and we end the paper with a new class of \(\frac{1}{\pi}\)-series. Our work is motivated by series recently discovered by Takeshi Sato.

MSC:

11Y60 Evaluation of number-theoretic constants
11F11 Holomorphic modular forms of integral weight
33C20 Generalized hypergeometric series, \({}_pF_q\)
33C05 Classical hypergeometric functions, \({}_2F_1\)
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