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

Part of: Entire and meromorphic functions, and related topics General field theory

Published online by Cambridge University Press:  09 April 2009

C. Frappier
C. Frappier
Affiliation:
Départment de Mathématiques et de Génie industriel École Polytechnique de Montréal Campus de l'Université de MontréalC.P. 6079, Succursale Centre-Ville Montréal (Québec)CanadaH3C 3A7 e-mail address: clement.frappier@courrier.polymtl.ca
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Abstract

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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.

MSC classification

Secondary: 30D10: Representations of entire functions by series and integrals 33C10: Bessel and Airy functions, cylinder functions, $_0F_1$ 12E10: Special polynomials
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 64 , Issue 3 , June 1998 , pp. 307 - 316
Copyright
Copyright © Australian Mathematical Society 1998

References

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