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Generalizations of the Bernoulli and Appell polynomials

Author

Listed:
  • Gabriella Bretti
  • Pierpaolo Natalini
  • Paolo E. Ricci

Abstract

We first introduce a generalization of the Bernoulli polynomials, and consequently of the Bernoulli numbers, starting from suitable generating functions related to a class of Mittag-Leffler functions. Furthermore, multidimensional extensions of the Bernoulli and Appell polynomials are derived generalizing the relevant generating functions, and using the Hermite-Kampé de Fériet (or Gould-Hopper) polynomials. The main properties of these polynomial sets are shown. In particular, the differential equations can be constructed by means of the factorization method.

Suggested Citation

  • Gabriella Bretti & Pierpaolo Natalini & Paolo E. Ricci, 2004. "Generalizations of the Bernoulli and Appell polynomials," Abstract and Applied Analysis, Hindawi, vol. 2004, pages 1-11, January.
    • Handle: RePEc:hin:jnlaaa:350120
    DOI: 10.1155/S1085337504306263
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    Cited by:

    1. Subuhi Khan & Nusrat Raza, 2013. "General-Appell Polynomials within the Context of Monomiality Principle," International Journal of Analysis, Hindawi, vol. 2013, pages 1-11, February.
    2. Francesco Aldo Costabile & Maria Italia Gualtieri & Anna Napoli, 2021. "General Bivariate Appell Polynomials via Matrix Calculus and Related Interpolation Hints," Mathematics, MDPI, vol. 9(9), pages 1-29, April.

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