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HYPERGEOMETRIC MODULAR EQUATIONS

Part of: Computational number theory Sequences and sets Discontinuous groups and automorphic forms

Published online by Cambridge University Press:  27 December 2018

SHAUN COOPER  and
WADIM ZUDILIN Open the ORCID record for WADIM ZUDILIN [Opens in a new window]
SHAUN COOPER
Affiliation:
Institute of Natural and Mathematical Sciences, Massey University – Albany, Private Bag 102904, North Shore Mail Centre, Auckland 0745, New Zealand email s.cooper@massey.ac.nz
WADIM ZUDILIN*
Affiliation:
Department of Mathematics, IMAPP, Radboud University, PO Box 9010, 6500 GL Nijmegen, Netherlands email w.zudilin@math.ru.nl School of Mathematical and Physical Sciences, The University of Newcastle, Callaghan, NSW 2308, Australia email wadim.zudilin@newcastle.edu.au
*
✉w.zudilin@math.ru.nl
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Abstract

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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 $1/\unicode[STIX]{x1D70B}$ and in the computation of mathematical constants.

Keywords

Ramanujan-type formulahypergeometric modular equations

MSC classification

Primary: 33C20: Generalized hypergeometric series, $_pF_q$
Secondary: 11B65: Binomial coefficients; factorials; $q$-identities 11F11: Holomorphic modular forms of integral weight 11Y60: Evaluation of constants

Information

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 107 , Issue 3 , December 2019 , pp. 338 - 366
Creative Commons
Creative Common License - CCCreative Common License - BY
This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited.
Copyright
© 2018 Australian Mathematical Publishing Association Inc.

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