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

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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 \(\lambda \)-Stirling numbers and two variables Hermite–Kampé de Fériet polynomials.

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Acknowledgments

The first Author was supported by Laboratoire d’Analyse et probalités du département de mathématiques de l’université d’Evry, and the second Author was supported, by the Scientific Research Project Administration of Akdeniz University.

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Authors and Affiliations

  1. Département de mathématiques, Université d’Evry Val d’Essonne, Bâtiment I.B.G.B.I., 3ème étage, 23 Bd. de France, 91037 , Evry Cedex, France

    Abdelmejid Bayad

  2. Department of Mathematics, Faculty of Arts and Science, University of Akdeniz, 07058 , Antalya, Turkey

    Yilmaz Simsek

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  1. Abdelmejid Bayad
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  2. Yilmaz Simsek
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Correspondence to Abdelmejid Bayad.

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Bayad, A., Simsek, Y. Convolution Identities on the Apostol–Hermite Base of Two Variables Polynomials. Differ Equ Dyn Syst 22, 309–318 (2014). https://doi.org/10.1007/s12591-013-0181-7

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  • DOI: https://doi.org/10.1007/s12591-013-0181-7

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