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

Bayad A., ŞİMŞEK Y.

Differential Equations and Dynamical Systems, cilt.22, sa.3, ss.309-318, 2014 (Scopus) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 22 Sayı: 3
  • Basım Tarihi: 2014
  • Doi Numarası: 10.1007/s12591-013-0181-7
  • Dergi Adı: Differential Equations and Dynamical Systems
  • Derginin Tarandığı İndeksler: Scopus
  • Sayfa Sayıları: ss.309-318
  • Anahtar Kelimeler: Apostol-Hermite polynomials, Convolution sums, Hermite-Kampé de Fériet, λ-Stirling numbers
  • Akdeniz Üniversitesi Adresli: Evet

Özet

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.