Journal of Applied Mathematics 
Volume 2003 (2003), Issue 3, Pages 155-163
doi:10.1155/S1110757X03204101

A generalization of the Bernoulli polynomials

Pierpaolo Natalini1 and Angela Bernardini2

 1Dipartimento di Matematica, Università degli Studi Roma III, Largo San Leonardo Murialdo 1, Roma 00146, Italy
2Departamento de Fisica y Matemática Aplicada, Universidad de Navarra, Pamplona E-30080, Spain
Received 16 April 2002; Revised 20 July 2002

Abstract

A generalization of the Bernoulli polynomials and, consequently, of the Bernoulli numbers, is defined starting from suitable generating functions. Furthermore, the differential equations of these new classes of polynomials are derived by means of the factorization method introduced by Infeld and Hull (1951).