A unified presentation of three families of generalized Apostol type polynomials based upon the theory of the umbral calculus and the umbral algebra

Dere R., ŞİMŞEK Y., Srivastava H. M.

JOURNAL OF NUMBER THEORY, vol.133, no.10, pp.3245-3263, 2013 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 133 Issue: 10
  • Publication Date: 2013
  • Doi Number: 10.1016/j.jnt.2013.03.004
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.3245-3263
  • Keywords: Bernoulli polynomials, Euler polynomials, Genocchi polynomials, Apostol-Bernoulli polynomials, Apostol-Euler polynomials, Apostol-Genocchi polynomials, Sheffer sequences, Appell sequences, Stirling numbers of the first and second kind, Multiplication formula, Recurrence formula, Umbral Calculus and Umbral Algebra, EULER POLYNOMIALS, GENOCCHI POLYNOMIALS, GENERATING-FUNCTIONS, Q-EXTENSIONS, MULTIPLICATION FORMULAS, MONOMIALITY PRINCIPLE, BERNOULLI POLYNOMIALS, FOURIER EXPANSIONS, NUMBERS, ZETA
  • Akdeniz University Affiliated: Yes


The aim of this paper is to introduce and investigate several new identities related to a unification and generalization of the three families of generalized Apostol type polynomials such as the Apostol-Bernoulli polynomials, the Apostol-Euler polynomials and the Apostol-Genocchi polynomials. The results presented here are based upon the theory of the Umbral Calculus and the Umbral Algebra. We also introduce some operators. By using a unified generating function for these Apostol type polynomials, which was constructed recently by Ozden et al. (2010) [42], we derive many new properties of these polynomials. Moreover, we give relations between. these polynomials and the Stirling numbers of the first and second kind. (C) 2013 Elsevier Inc. All rights reserved.