Some new results on products of Apostol-Bernoulli and Apostol-Euler polynomials

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:431

Article

He, Yuan

关键词: Apostol-Bernoulli polynomials and numbers;    Apostol-Euler polynomials and numbers;    Convolution formulae;    Recurrence formulae;   

DOI  :  10.1016/j.jmaa.2015.05.055

来源: Elsevier

【 摘 要 】

We perform a further investigation for the Apostol-Bernoulli and Apostol-Euler polynomials and numbers. By making use of an elementary idea used by Euler in the discovery of his famous Pentagonal Number Theorem, we establish some new formulae for products of an arbitrary number of Apostol-Bernoulli and Apostol-Euler polynomials and numbers. These results are the corresponding generalizations of some known formulae including the higher-order convolution ones discovered by Agoh and Dilcher (2014) [5] on the classical Bernoulli and Euler polynomials. (C) 2015 Elsevier Inc. All rights reserved.

【 授权许可】

Free