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Hermite base Bernoulli type polynomials on the umbral algebra

Russian Journal of Mathematical Physics volume 22, pages 1–5 (2015)Cite this article

Abstract

The aim of this paper is to construct new generating functions for Hermite base Bernoulli type polynomials, which generalize not only the Milne-Thomson polynomials but also the two-variable Hermite polynomials. We also modify the Milne-Thomson polynomials, which are related to the Bernoulli polynomials and the Hermite polynomials. Moreover, by applying the umbral algebra to these generating functions, we derive new identities for the Bernoulli polynomials of higher order, the Hermite polynomials and numbers of higher order, and the Stirling numbers of the second kind.

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Science University of Akdeniz, TR-07058, Antalya, Turkey

    R. Dere & Y. Simsek

Authors
  1. R. Dere
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  2. Y. Simsek
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Correspondence to R. Dere.

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Dere, R., Simsek, Y. Hermite base Bernoulli type polynomials on the umbral algebra. Russ. J. Math. Phys. 22, 1–5 (2015). https://doi.org/10.1134/S106192081501001X

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  • DOI: https://doi.org/10.1134/S106192081501001X

Keywords

  • Mathematical Physic
  • Hermite Polynomial
  • Bernoulli Polynomial
  • Stirling Number
  • Quantum Harmonic Oscillator