標題: New analogues of Clausen's identities arising from the theory of modular forms
作者: Chan, Heng Huat
Tanigawa, Yoshio
Yang, Yifan
Zudilin, Wadim
應用數學系
Department of Applied Mathematics
關鍵字: Clausen's identities;Modular forms of one variable
公開日期: 1-十月-2011
摘要: Around 1828, T. Clausen discovered that the square of certain hypergeometric (2)F(1) function can be expressed as a hypergeometric (3)F(2) function. Special cases of Clausen's identities were later used by S. Ramanujan in his derivation of 17 series for 1/pi. 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/pi. 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. (C) 2011 Elsevier Inc. All rights reserved.
URI: http://dx.doi.org/10.1016/j.aim.2011.06.011
http://hdl.handle.net/11536/18971
ISSN: 0001-8708
DOI: 10.1016/j.aim.2011.06.011
期刊: ADVANCES IN MATHEMATICS
Volume: 228
Issue: 2
起始頁: 1294
結束頁: 1314
顯示於類別:期刊論文


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  1. 000293667800017.pdf