Some relationships between the generalized Apostol-Bernoulli polynomials and Hurwitz-Lerch Zeta functions

被引：96

作者：

Garg, Mridula

Jain, Kumkum

Srivastava, H. M. ^{[1
]}

机构：

[1] Univ Victoria, Dept Math & Stat, Victoria, BC V8W 3P4, Canada

[2] Univ Rajasthan, Dept Math, Jaipur 302004, Rajasthan, India

来源：

INTEGRAL TRANSFORMS AND SPECIAL FUNCTIONS | 2006年 / 17卷 / 11期

基金：

加拿大自然科学与工程研究理事会;

关键词：

Bernoulli polynomials; Apostol-Bernoulli polynomials; Apostol-Bernoulli polynomials of higher order; Apostol-Euler polynomials of higher order; Bernoulli numbers of higher order; Apostol-Bernoulli numbers of higher order; Hurwitz (or generalized) Zeta function; Hurwitz-Lerch and Lipschitz-Lerch Zeta functions; Lerch's functional equation (or Lerch's transformation formula);

D O I：

10.1080/10652460600926907

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The main object of this paper is to further investigate the generalized Apostol-Bernoulli polynomials of higher order, which were introduced and studied recently by Luo and Srivastava [2005, Journal of Mathematical Analysis and Applications, 308, 290 - 302; 2006, Computers and Mathematics with Applications, 51, 631 - 642]. Here, we first derive an explicit representation of these generalized Apostol - Bernoulli polynomials of higher order in terms of a generalization of the Hurwitz - Lerch Zeta function and then proceed to establish a functional relationship between the generalized Apostol Bernoulli polynomials of rational arguments and the Hurwitz ( or generalized) Zeta function. Our results would provide extensions of those given earlier by ( for example) Apostol [ 1951, Pacific Journal of Mathematics, 1, 161 - 167] and Srivastava [ 2000, Mathematical Proceedings of the Cambridge Philosophical Society, 129, 77 - 84].

引用

页码：803 / 815

页数：13

共 19 条

[1]

APOSTOL TM, 1951, B AM MATH SOC, V57, P370

[2]

Apostol TM., 1998, INTRO ANAL NUMBER TH

[3]

Erdelyi A., 1954, TABLES INTEGRAL TRAN, VII

[4]

Erdelyi A., 1953, HIGHER TRANSCENDENTA, VII