On the Apostol-Bernoulli polynomials
type: Item
instance of: scholarly article
title: On the Apostol-Bernoulli polynomials
zbMATH Open document ID: 1073.33001
DOI: 10.2478/BF02475959
author: Qiu-Ming Luo
published in: Central European Journal of Mathematics
publication date: 2005-03-11T00:00:00Z
review text: In an earlier paper [Math. Proc. Camb. Philos. Soc. 129, No. 1, 77--84 (2000; Zbl 0978.11004)], the reviewer gave explicit representations of the general Hurwitz-Lerch zeta function and the Apostol-Bernoulli polynomials \({\mathcal B}_n(x;\lambda)\) [see \textit{T. M. Apostol}, Pac. J. Math. 1, 161--167 (1951; Zbl 0043.07103)] in finite series of the Hurwitz (or generalized) zeta function \(\zeta(s, a)\). The present author repeats much of what is already contained in the reviewer's paper. He also derives some standard properties of the Apostol-Bernoulli polynomials \({\mathcal B}_n(x;\lambda)\). One of these properties extends a result of the reviewer and \textit{P. G. Todorov} [J. Math. Anal. Appl. 130, No. 2, 509--513 (1988; Zbl 0621.33008)].
Mathematics Subject Classification ID: 11B68
Mathematics Subject Classification ID: 11M35
Mathematics Subject Classification ID: 33C05
zbMATH DE Number: 2143668
zbMATH Keywords: Bernoulli numbers
zbMATH Keywords: Bernoulli polynomials
zbMATH Keywords: Apostol-Bernoulli numbers
zbMATH Keywords: Apostol-Bernoulli polynomials
zbMATH Keywords: Gaussian hypergeometric functions
zbMATH Keywords: Stirling numbers of the second kind
zbMATH Keywords: Hurwitz zeta function
zbMATH Keywords: Lerch functional equation
reviewed by: H. M. Srivastava
MaRDI profile type: Publication
cites work: On the Lerch zeta function
cites work: Q4101884
cites work: Q4769056
cites work: Some formulas for the Bernoulli and Euler polynomials at rational arguments
cites work: Series associated with the zeta and related functions
cites work: An explicit formula for the generalized Bernoulli polynomials
cites work: Explicit Formulas for Bernoulli Numbers
cites work: Apostol-Euler polynomials of higher order and Gaussian hypergeometric functions
cites work: New Formulae for the Bernoulli and Euler Polynomials at Rational Arguments
description: scientific article; zbMATH DE number 2143668