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arXiv:0812.1303 [math.NT]AbstractReferencesReviewsResources

On the Taylor Coefficients of the Hurwitz Zeta Function

Khristo Boyadzhiev

Published 2008-12-06Version 1

We find a representation for the Maclaurin coefficients of the Hurwitz zeta-function in terms of semi-convergent series involving the Bernoulli polynomials and the Stirling numbers of the first kind. In particular, this gives a representation for the coefficients of the Riemann zeta function. Our main instrument is a certain series transformation formula. A similar result is proved also for the Maclaurin coefficients of the Lerch zeta function.

Comments: 9 pages. To appear in the JP Journal of Algebra, Number Theory and Applications
Categories: math.NT, math.CA
Subjects: 11M35, 33A70
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