On the Apostol-Bernoulli Polynomials

被引：44

作者：

Luo, Qiu-Ming ^{[1
]}

机构：

[1] Jiaozuo Univ, Dept Math, Jiaozuo City 454003, Henan, Peoples R China

来源：

CENTRAL EUROPEAN JOURNAL OF MATHEMATICS | 2004年 / 2卷 / 04期

关键词：

Bernoulli numbers; Bernoulli polynomials; Apostol-Bernoulli numbers; Apostol-Bernoulli polynomials; Gaussian hypergeometric functions; Stirling numbers of the second kind; Hurwitz Zeta functions; Lerch functional equation;

D O I：

10.2478/BF02475959

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In the present paper, we obtain two new formulas of the Apostol-Bernoulli polynomials (see On the Lerch Zeta function. Pacific J. Math., 1 (1951), 161-167.), using the Gaussian hypergeometric functions and Hurwitz Zeta functions respectively, and give certain special cases and applications. (C) Central European Science Journals. All rights reserved.

引用

页码：509 / 515

页数：7

共 10 条

[1] Abramowitz M., 1965, APPL MATH SERIES, V55
[2] APOSTOL TM, 1951, B AM MATH SOC, V57, P370
[3] Apostol TM., 1998, INTRO ANAL NUMBER TH
[4] Comtet L., 1974, ADV COMBINATORICS AR
[5] NEW FORMULAS FOR THE BERNOULLI AND EULER POLYNOMIALS AT RATIONAL ARGUMENTS
CVIJOVIC, D
KLINOWSKI, J
[J]. PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1995, 123 (05) : 1527 - 1535
[6] EXPLICIT FORMULAS FOR BERNOULLI NUMBERS
GOULD, HW
[J]. AMERICAN MATHEMATICAL MONTHLY, 1972, 79 (01) : 44 - &
[7] Qiu-Ming Luo, BERNOULLI POLY UNPUB
[8] Srivastava H.M., 2001, Series associated with the Zeta and related functions
[9] Some formulas for the Bernoulli and Euler polynomials at rational arguments
Srivastava, HM
[J]. MATHEMATICAL PROCEEDINGS OF THE CAMBRIDGE PHILOSOPHICAL SOCIETY, 2000, 129 : 77 - 84
[10] AN EXPLICIT FORMULA FOR THE GENERALIZED BERNOULLI POLYNOMIALS
SRIVASTAVA, HM
TODOROV, PG
[J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 1988, 130 (02) : 509 - 513

← 1 →