On the Apostol-Bernoulli polynomials
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)].
scientific article; zbMATH DE number 2143668