ON AN INTRIGUING INTEGRAL AND SOME SERIES RELATED TO ZETA(4)

被引：75

作者：

BORWEIN, D ^{[1
]}

BORWEIN, JM ^{[1
]}

机构：

[1] SIMON FRASER UNIV,DEPT MATH & STAT,BURNABY,BC V5A 1S6,CANADA

来源：

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY | 1995年 / 123卷 / 04期

关键词：

RIEMANN ZETA FUNCTION; PARSEVALS IDENTITY; GENERATING FUNCTIONS; LOGCOSINE INTEGRALS; POLYLOGARITHMS;

D O I：

10.2307/2160718

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

An intriguing log-cosine integral is fully analyzed and shown to have value a rational multiple of pi zeta(4), zeta being the Riemann zeta function. From this we deduce by means of generating functions and Parseval's identity the sums of certain series previously established by a completely different method.

引用

页码：1191 / 1198

页数：8