Hypergeometric modular equations

Cooper, Shaun; Zudilin, Wadim

doi:10.1017/S144678871800037X

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Hypergeometric modular equations

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Zudilin, Wadim
Max Planck Institute for Mathematics, Max Planck Society;

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https://doi.org/10.1017/S144678871800037X
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Cooper-Zudilin_Hypergeometric modular equations_2019.pdf
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Citation

Cooper, S., & Zudilin, W. (2019). Hypergeometric modular equations. Journal of the Australian Mathematical Society, 107(3), 338-366. doi:10.1017/S144678871800037X.

Cite as: https://hdl.handle.net/21.11116/0000-0006-91EE-A

Abstract

We record $$ \binom{42}2+\binom{23}2+\binom{13}2=1192 $$ functional
identities that, apart from being amazingly amusing by themselves, find
applications in derivation of Ramanujan-type formulas for $1/\pi$ and in
computation of mathematical constants.