Rational analogues of Ramanujan's series for 1/π

被引：26

作者：

Chan, Heng Huat ^{[1
]}

Cooper, Shaun ^{[2
]}

机构：

[1] Natl Univ Singapore, Dept Math, Singapore 117543, Singapore

[2] Massey Univ Albany, Inst Informat & Math Sci, N Shore Mail Ctr, Auckland, New Zealand

来源：

MATHEMATICAL PROCEEDINGS OF THE CAMBRIDGE PHILOSOPHICAL SOCIETY | 2012年 / 153卷

关键词：

MODULAR EQUATIONS; SIMPLE PROOF; FORMULAS; TRANSFORMATIONS; APPROXIMATIONS; IDENTITY; NUMBERS;

D O I：

10.1017/S0305004112000254

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

A general theorem is stated that unifies 93 rational Ramanujan-type series for 1/pi, 40 of which are believed to be new. Moreover, each series is shown to have a companion identity, thereby giving another 93 series, the majority of which are new.

引用

页码：361 / 383

页数：23

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