Probabilistic Proofs of Some Relationships Between the Bernoulli and Euler Polynomials

Authors

  • H.M. Srivastava
  • Christophe Vignat

Keywords:

Bernoulli polynomials, Euler polynomials, Generating functions, Probabilistic proofs, Umbral calculus.

Abstract

The main purpose of this article is to provide probabilistic proofs of the relationships between the generalized Bernoulli (or Norlund) polynomials B() n (x) and the generalized Euler polynomials E() n (x) of (real or complex) order and degree n in x, which were proved recently by Srivastava and Pintér [11]. Some other approaches to these relationships and their seemingly interesting generalizationsare also investigated.

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Published

2012-05-14

Issue

Vol. 5 No. 2: (April 2012)

Section

Complex Analysis

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How to Cite

Probabilistic Proofs of Some Relationships Between the Bernoulli and Euler Polynomials. (2012). European Journal of Pure and Applied Mathematics, 5(2), 97-107. https://www.ejpam.com/index.php/ejpam/article/view/1596