Representation formulas for entire functions
of exponential type and generalized Bernoulli polynomials

C. Frappier
Département de Mathématiques et de Génie industriel
École Polytechnique de Montréal
Campus de l'Université de Montréal
C.P. 6079, Succursale Centre-Ville
Montréal (Québec)
Canada H3C 3A7
e-mail address: clement.frappier@courrier.polymtl.ca

Abstract:

We introduce a sequence of polynomials which are extensions of the classic Bernoulli polynomials. This generalization is obtained by using the Bessel functions of the first kind. We use these polynomials to evaluate explicitly a general class of series containing an entire function of exponential type.