On some expansions, involving falling factorials, for the Euler Gamma function and the Riemann Zeta function

Details On some expansions, involving falling factorials, for the Euler Gamma function and the Riemann Zeta function On some expansions, involving falling factorials, for the Euler Gamma function and the Riemann Zeta function

2010-07-12

arxiv.org/abs/1007.1955v1

Mathematics

Classical Analysis and ODEs

Preprint

Scientific paper

In the present paper we introduce some expansions for the Euler Gamma
function and the Riemann Zeta function. The expansions involve the falling
factorials. In the proofs we use the Faa di Bruno formula, Bell polynomials,
Potential polynomials, Mittag-Leffler polynomials, derivative polynomials and
special numbers (Eulerian numbers and Stirling numbers of both kinds).

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