Open Access

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

Journal of Inequalities and Applications20062006:48727

https://doi.org/10.1155/JIA/2006/48727

Received: 29 June 2005

Accepted: 3 July 2005

Published: 13 April 2006

Abstract

We denote by and the gamma and the incomplete gamma functions, respectively. In this paper we prove some monotonicity results for the gamma function and extend, to , a lower bound established by Elbert and Laforgia (2000) for the function , with , only for .

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Authors’ Affiliations

(1)
Department of Mathematics, Roma Tre University

References

  1. Alzer H: On some inequalities for the incomplete gamma function. Mathematics of Computation 1997,66(218):771–778. 10.1090/S0025-5718-97-00814-4MATHMathSciNetView ArticleGoogle Scholar
  2. Elbert Á, Laforgia A: An inequality for the product of two integrals relating to the incomplete gamma function. Journal of Inequalities and Applications 2000,5(1):39–51. 10.1155/S1025583400000035MATHMathSciNetGoogle Scholar
  3. Gautschi W: Some elementary inequalities relating to the gamma and incomplete gamma function. Journal of Mathematics and Physics 1959, 38: 77–81.MATHMathSciNetView ArticleGoogle Scholar
  4. Kershaw D, Laforgia A: Monotonicity results for the gamma function. Atti della Accademia delle Scienze di Torino. Classe di Scienze Fisiche, Matematiche e Naturali 1985,119(3–4):127–133 (1986).MATHMathSciNetGoogle Scholar
  5. Qi F, Guo S-L: Inequalities for the incomplete gamma and related functions. Mathematical Inequalities & Applications 1999,2(1):47–53.MATHMathSciNetView ArticleGoogle Scholar

Copyright

© A. Laforgia and P. Natalini. 2006

This article is published under license to BioMed Central Ltd. 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.