Journal of Inequalities and Applications
Volume 2006 (2006), Article ID 48727, 8 pages

Supplements to known monotonicity results and inequalities for the gamma and incomplete gamma functions

A. Laforgia and P. Natalini

Department of Mathematics, Roma Tre University, Largo San Leonardo Murialdo 1, Rome 00146, Italy

Received 29 June 2005; Accepted 3 July 2005

Copyright © 2006 A. Laforgia and P. Natalini. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We denote by Γ(a) and Γ(a;z) the gamma and the incomplete gamma functions, respectively. In this paper we prove some monotonicity results for the gamma function and extend, to x>0, a lower bound established by Elbert and Laforgia (2000) for the function 0xetpdt=[Γ(1/p)Γ(1/p;xp)]/p, with p>1, only for 0<x<(9(3p+1)/4(2p+1))1/p.