New analogues of Clausen’s identities arising from the theory of modular forms

Title: New analogues of Clausen’s identities arising from the theory of modular forms
Creator: Chan, Heng Huat; Tanigawa, Yoshio; Yang, Yifan; Zudilin, W.
Relation: Advances in Mathematics Vol. 228, Issue 2, p. 1294-1314
Publisher Link: http://dx.doi.org/10.1016/j.aim.2011.06.011
Publisher: Academic Press
Resource Type: journal article
Date: 2011
Description: Around 1828, T. Clausen discovered that the square of certain hypergeometric ₂F₁ function can be expressed as a hypergeometric ₃F₂ function. Special cases of Clausen’s identities were later used by S. Ramanujan in his derivation of 17 series for 1/π. Since then, there were several attempts to find new analogues of Clausen’s identities with the hope to derive new classes of series for 1/π. Unfortunately, none were successful. In this article, we will present three new analogues of Clausen’s identities. Their discovery is motivated by the study of relations between modular forms of weight 2 and modular functions associated with modular groups of genus 0.
Subject: Clausen’s identities; modular forms of one variable
Identifier: http://hdl.handle.net/1959.13/934806
Identifier: uon:11910
Identifier: ISSN:0001-8708
Language: eng
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