New analogues of Clausen's identities arising from the theory of modular forms
Journal
Advances in Mathematics
Journal Volume
228
Journal Issue
2
Pages
1294-1314
Date Issued
2011
Author(s)
Chan, H.H.
Tanigawa, Y.
Yang, Y.
Zudilin, Wadim
Abstract
Around 1828, T. Clausen discovered that the square of certain hypergeometric F12 function can be expressed as a hypergeometric F23 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. © 2011 Elsevier Inc.
SDGs
Type
journal article