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Some representation formulae for entire functions of exponential type

Published online by Cambridge University Press:  17 April 2009

Clément Frappier
Clément Frappier
Affiliation:
Départment de Mathématiques Appliquées, École Polytechnique de Montréal, Campus de l'Université de Montréal, Case Postale 6079, Succursale “A”, Monteéal, Québec, H3C 3A7, Canada
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Abstract

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We obtain some explicit formulae for series of the type

where f is an entire function of exponential type τ, bounded on the real exis (and satisfying in the first case). These series are expressed in terms of the derivatives of f and Bernoulli numbers. We examine the case where f is a trigonometric polynomial which lead us, in particular, to a new representation of the associated Fejér mean.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 37 , Issue 1 , February 1988 , pp. 17 - 26
Copyright
Copyright © Australian Mathematical Society 1988

References

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