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

共 50 条

[21] Some computational formulas related the Riemann zeta-function tails [J].

Xu, Hongmin .

JOURNAL OF INEQUALITIES AND APPLICATIONS, 2016,

[22] A new integral representation of the Riemann zeta function [J].

Wu, YF .

ROCKY MOUNTAIN JOURNAL OF MATHEMATICS, 2004, 34 (03) :1177-1189

[23] A triple integral analog of a multiple zeta value [J].

Amdeberhan, Tewodros ;

Moll, Victor H. ;

Straub, Armin ;

Vignat, Christophe .

INTERNATIONAL JOURNAL OF NUMBER THEORY, 2021, 17 (02) :223-237

[24] ON VALUES OF THE RIEMANN ZETA FUNCTION AT INTEGRAL ARGUMENTS [J].

EWELL, JA .

CANADIAN MATHEMATICAL BULLETIN-BULLETIN CANADIEN DE MATHEMATIQUES, 1991, 34 (01) :60-66

[25] Some classes of infinite series associated with the Riemann Zeta and Polygamma functions and generalized harmonic numbers [J].

Rassias, TM ;

Srivastava, HM .

APPLIED MATHEMATICS AND COMPUTATION, 2002, 131 (2-3) :593-605

[26] More series related to the Euler series [J].

Ogreid, OM ;

Osland, P .

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2001, 136 (1-2) :389-403

[27] On integral representations for powers of the Riemann zeta-function [J].

Ivic, A .

PUBLICATIONES MATHEMATICAE-DEBRECEN, 1998, 52 (3-4) :469-495

[28] The Euler-Riemann zeta function in some series formulae and its values at odd integer points [J].

Stevanovic, Milorad R. ;

Petrovic, Predrag B. .

JOURNAL OF NUMBER THEORY, 2017, 180 :769-786

[29] On some log-cosine integrals related to ζ(3), ζ(4), and ζ(6) [J].

Coffey, MW .

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2003, 159 (02) :205-215

[30] THE RIEMANN ZETA FUNCTION AND CLASSES OF INFINITE SERIES [J].

Alzer, Horst ;

Choi, Junesang .

APPLICABLE ANALYSIS AND DISCRETE MATHEMATICS, 2017, 11 (02) :386-398

← 1 2 3 4 5 →