On some expansions for the Euler Gamma function and the Riemann Zeta function

[摘要] In the present paper we introduce some expansions which use the falling factorials for the Euler Gamma function and the Riemann Zeta function. 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). We investigate the rate of convergence of the series and give some numerical examples. (c) 2011 Elsevier B.V. All rights reserved.

[发布日期] 2012-09-01

[效力级别]  Proceedings Paper

[关键词] Euler Gamma function;Riemann Zeta function;Bell polynomials;Potential polynomials;Mittag-Leffler polynomials;Derivative polynomials