On some expansions for the Euler Gamma function and the Riemann Zeta function
Classical Analysis and ODEs
2013-02-14 v2 Combinatorics
Abstract
In the present paper we introduce some expansions, based on the falling factorials, for the Euler Gamma function and the Riemann Zeta function. In the proofs we use the Fa\'a di Bruno formula, Bell polynomials, potential polynomials, Mittag-Leffler polynomials, derivative polynomials and special numbers (Eulerian numbers and Stirling numbers of both kinds). We investigate the rate of convergence of the series and give some numerical examples.
Cite
@article{arxiv.1007.1955,
title = {On some expansions for the Euler Gamma function and the Riemann Zeta function},
author = {Grzegorz Rzadkowski},
journal= {arXiv preprint arXiv:1007.1955},
year = {2013}
}
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Published article