On Some Asymptotic Expansions for the Gamma Function

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

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 Faá 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 con...

On Some Inequalities for the Gamma Function

We present some elementary proofs of well-known inequalities for the gamma function and for the ratio of two gamma functions. The paper is purely expository and it is based on the talk that the first author gave during the memorial conference in Patras, 2012.

Asymptotic expansions for ratios of products of gamma functions

An asymptotic expansion for a ratio of products of gamma functions is derived. 2000 Mathematics Subject Classification: Primary 33B15; Secondary 33C20

Asymptotic Expansions of the Gamma Function Associated with the Windschitl and Smith Formulas

In this paper, we develop the Windschitl and Smith formulas for the gamma function to complete asymptotic expansions and provide explicit formulas for determining the coefficients of these asymptotic expansions. Furthermore, we establish new asymptotic expansions for the ratio of gamma functions Γ(x + 1)/Γ(x + 1 2 ).

Asymptotic Expansions for Integrals