ON THE VALUES OF A CLASS OF DIRICHLET SERIES AT RATIONAL ARGUMENTS

被引：3

作者：

Chakraborty, K. ^{[1
]}

Kanemitsu, S. ^{[2
]}

Li, H-L ^{[3
]}

机构：

[1] Harish Chandra Res Inst, Allahabad 211019, Uttar Pradesh, India

[2] Kinki Univ, Grad Sch Adv Technol, Fukuoka 8208555, Japan

[3] Weinan Teachers Coll, Dept Math, Weinan 714000, Shaanxi, Peoples R China

来源：

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY | 2010年 / 138卷 / 04期

关键词：

Lipschitz-Lerch transcendent; Hurwitz zeta function; polylogarithm function; Gauss' second formula; Milnor's gamma function; EULER POLYNOMIALS; BERNOULLI; FORMULAS;

D O I：

10.1090/S0002-9939-09-10171-5

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper we shall prove that the combination of the general distribution property and the functional equation for the Lipschitz-Lerch transcendent capture the whole spectrum of deeper results on the relations between the values at rational arguments of functions of a class of zeta-functions. By Theorem I and its corollaries, we can cover all the previous results in a rather simple and lucid way. By considering the limiting cases, we can also deduce new striking identities for Milnor's gamma functions, among which is the Gauss second formula for the digamma function.

引用

页码：1223 / 1230

页数：8

共 13 条

[1]

[Anonymous], KOBE J MATH

[2]

Apostol T.M., 1976, INTRO ANAL NUMBER TH

[3] CLOSED-FORM SUMMATION OF SOME TRIGONOMETRIC SERIES [J].

CVIJOVIC, D ;

KLINOWSKI, J .

MATHEMATICS OF COMPUTATION, 1995, 64 (209) :205-210

[4] NEW FORMULAS FOR THE BERNOULLI AND EULER POLYNOMIALS AT RATIONAL ARGUMENTS [J].

CVIJOVIC, D ;

KLINOWSKI, J .

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1995, 123 (05) :1527-1535

[5]

Kanemitsu S., 2007, Vistas of Special Functions

[6]

KANEMITSU S, 1989, EVALUATION CERTAIN L, P459

[7]

Lewin L., 1981, Polylogarithms and associated functions

[8]

LI HL, STRUCTURAL IN PRESS

[9]

Milnor J., 1983, Enseign. Math, V29, P281

[10] Transcendental values of the digamma function [J].

Murty, M. Ram ;

Saradha, N. .

JOURNAL OF NUMBER THEORY, 2007, 125 (02) :298-318

← 1 2 →