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Generalised Bernoulli polynomials and series
Published online by Cambridge University Press: 17 April 2009
Abstract
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.
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- Copyright © Australian Mathematical Society 2000
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