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Generalised Bernoulli polynomials and series

Published online by Cambridge University Press:  17 April 2009

Clément Frappier
Clément Frappier
Affiliation:
Département de Mathématiques et de Génie Industriel, École Polytechnique de Montréal, Case postale 6079, Succursale Centre-Ville, Montreal (Quebec), Canada H3C 3A7, e-mail: clement.frappier@courier.polymtl.ca
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Abstract

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We present several results related to the recently introduced generalised Bernoulli polynomials. Some recurrence relations are given, which permit us to compute efficiently the polynomials in question. The sums , where jk = jk (α) are the zeros of the Bessel function of the first kind of order α, are evaluated in terms of these polynomials. We also study a generalisation of the series appearing in the Euler-MacLaurin summation formula.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 61 , Issue 2 , April 2000 , pp. 289 - 304
Copyright
Copyright © Australian Mathematical Society 2000

References

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