English

On the Taylor Coefficients of the Hurwitz Zeta Function

Number Theory 2008-12-09 v1 Classical Analysis and ODEs

Abstract

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.

Keywords

Cite

@article{arxiv.0812.1303,
  title  = {On the Taylor Coefficients of the Hurwitz Zeta Function},
  author = {Khristo Boyadzhiev},
  journal= {arXiv preprint arXiv:0812.1303},
  year   = {2008}
}

Comments

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