On the Taylor Coefficients of the Hurwitz Zeta Function

Details On the Taylor Coefficients of the Hurwitz Zeta Function On the Taylor Coefficients of the Hurwitz Zeta Function

2008-12-06

arxiv.org/abs/0812.1303v1

Mathematics

Number Theory

9 pages. To appear in the JP Journal of Algebra, Number Theory and Applications

Scientific paper

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.

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