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 |