The Hurwitz zeta function as a convergent series

被引：4

作者：

Dwilewicz, Roman ^{[1
]}

Minac, Jan

机构：

[1] Univ Missouri, Dept Math & Stat, Rolla, MO 65409 USA

[2] Polish Acad Sci, Inst Math, PL-00956 Warsaw, Poland

[3] Univ Western Ontario, Dept Math, London, ON N6A 5B7, Canada

来源：

ROCKY MOUNTAIN JOURNAL OF MATHEMATICS | 2006年 / 36卷 / 04期

关键词：

Hurwitz zeta function; Bernoulli polynomials; Bernoulli numbers;

D O I：

10.1216/rmjm/1181069411

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

New series for the Hurwitz zeta function which converge on the whole plane, except s = 1, are developed. This is applied to obtain a remarkably simple evaluation of some special values of the function.

引用

页码：1191 / 1219

页数：29

共 50 条

[1] On some slowly convergent series involving the Hurwitz zeta-function
Hashimoto, M
Kanemitsu, S
Tanigawa, Y
Yoshimoto, M
Zhang, WP
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2003, 160 (1-2) : 113 - 123
[2] Hyperharmonic series involving Hurwitz zeta function
Mezo, Istvan
Dil, Ayhan
JOURNAL OF NUMBER THEORY, 2010, 130 (02) : 360 - 369
[3] On some series representations of the Hurwitz zeta function
Coffey, Mark W.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2008, 216 (01) : 297 - 305
[4] A Series Representation for the Hurwitz-Lerch Zeta Function
Reynolds, Robert
Stauffer, Allan
AXIOMS, 2021, 10 (04)
[5] The Hurwitz Zeta Function and the Lerch Zeta Function
Fraczek, Markus Szymon
SELBERG ZETA FUNCTIONS AND TRANSFER OPERATORS: AN EXPERIMENTAL APPROACH TO SINGULAR PERTURBATIONS, 2017, 2139 : 43 - 68
[6] HYPERGEOMETRIC SERIES ASSOCIATED WITH THE HURWITZ-LERCH ZETA FUNCTION
Bin-Saad, M. G.
ACTA MATHEMATICA UNIVERSITATIS COMENIANAE, 2009, 78 (02): : 269 - 286
[7] A New Family of Zeta Type Functions Involving the Hurwitz Zeta Function and the Alternating Hurwitz Zeta Function
Kim, Daeyeoul
Simsek, Yilmaz
MATHEMATICS, 2021, 9 (03) : 1 - 11
[8] ON THE HURWITZ ZETA-FUNCTION
GUO, JB
CHINESE SCIENCE BULLETIN, 1991, 36 (19): : 1666 - 1667
[9] Inequalities for the Hurwitz zeta function
Alzer, H
PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS, 2000, 130 : 1227 - 1236
[10] ON HURWITZ ZETA-FUNCTION
RANE, VV
MATHEMATISCHE ANNALEN, 1983, 264 (02) : 147 - 151

← 1 2 3 4 5 →