Convolution Identities on the Apostol-Hermite Base of Two Variables Polynomials


Bayad A., ŞİMŞEK Y.

Differential Equations and Dynamical Systems, vol.22, no.3, pp.309-318, 2014 (Scopus) identifier

  • Publication Type: Article / Article
  • Volume: 22 Issue: 3
  • Publication Date: 2014
  • Doi Number: 10.1007/s12591-013-0181-7
  • Journal Name: Differential Equations and Dynamical Systems
  • Journal Indexes: Scopus
  • Page Numbers: pp.309-318
  • Keywords: Apostol-Hermite polynomials, Convolution sums, Hermite-Kampé de Fériet, λ-Stirling numbers
  • Akdeniz University Affiliated: Yes

Abstract

In this paper, we introduce a linear differential operator and investigate its fundamental properties. By means of this operator we derive convolution identities for Apostol-Hermite base two variables polynomials. These identities extend the Euler's identities for the sums of product for the two variables Hermite base Apostol-Bernoulli and Apostol-Euler polynomials. Applying this differential operator to some specials functions, we obtain interesting identities and formulae involving the two variables Hermite base Apostol-Bernoulli and two variables Hermite base Apostol-Euler polynomials arising from the λ-Stirling numbers and two variables Hermite-Kampé de Fériet polynomials. © 2013 Foundation for Scientific Research and Technological Innovation.