Some families of the Hurwitz-Lerch Zeta functions and associated fractional derivative and other integral representations

被引：117

作者：

Lin, SD

Srivastava, HM ^{[1
]}

机构：

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

[2] Chung Yuan Christian Univ, Dept Appl Math, Chungli 32023, Taiwan

来源：

APPLIED MATHEMATICS AND COMPUTATION | 2004年 / 154卷 / 03期

基金：

加拿大自然科学与工程研究理事会;

关键词：

Hurwitz-Lerch Zeta functions; Riemann-Liouville fractional derivative; sum-integral representations; Fox-Wright generalized hypergeometric function; Gauss hypergeometric function; Euler transformation; Eulerian integral of the second kind; Hankel's loop; Mellin-Barnes contour;

D O I：

10.1016/S0096-3003(03)00746-X

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 present, in a unified manner, a number of fractional derivative and other integral representations for several general families of the Hurwitz-Lerch Zeta functions. Relevant connections of the results presented here with those obtained in earlier works are also indicated precisely. (C) 2003 Elsevier Inc. All rights reserved.

引用

页码：725 / 733

页数：9

共 10 条

[1]

[Anonymous], J FRACT CALC

[2]

Erdelyi A., 1954, TABLES INTEGRAL TRAN, VII

[3]

Erdelyi A., 1953, HIGHER TRANSCENDENTA, VII

[4]

Goyal S. P., 1997, Ganita Sandesh, V11, P99

[5]

Polubny I., 1999, MATH SCI ENG, V198

[6]

Srivastava H.M., 2001, Series associated with the Zeta and related functions

[7] A certain class of generating functions involving bilateral series [J].

Srivastava, HM ;

Pathan, MA ;

Bin-Saad, MG .

ANZIAM JOURNAL, 2003, 44 :475-483

[8]

Whittaker E. T., 1927, A Course on Modern Analysis. An Introduction to the General Theory of Infinite Processes and of Analytical Functions

[9]

with an Account of the Principal Transcendental Functions

[10]

YEN CE, 2002, J FRACT CALC, V22, P99

← 1 →