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Journal of Inequalities and Applications
Published in: Journal of Inequalities and Applications 1/2006

Open Access 01-12-2006 | Research Article

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

Authors: A. Laforgia, P. Natalini

Published in: Journal of Inequalities and Applications | Issue 1/2006

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Abstract

We denote by https://static-content.springer.com/image/art%3A10.1155%2FJIA%2F2006%2F48727/MediaObjects/13660_2005_Article_1604_IEq1_HTML.gif and https://static-content.springer.com/image/art%3A10.1155%2FJIA%2F2006%2F48727/MediaObjects/13660_2005_Article_1604_IEq2_HTML.gif the gamma and the incomplete gamma functions, respectively. In this paper we prove some monotonicity results for the gamma function and extend, to https://static-content.springer.com/image/art%3A10.1155%2FJIA%2F2006%2F48727/MediaObjects/13660_2005_Article_1604_IEq3_HTML.gif , a lower bound established by Elbert and Laforgia (2000) for the function https://static-content.springer.com/image/art%3A10.1155%2FJIA%2F2006%2F48727/MediaObjects/13660_2005_Article_1604_IEq4_HTML.gif , with https://static-content.springer.com/image/art%3A10.1155%2FJIA%2F2006%2F48727/MediaObjects/13660_2005_Article_1604_IEq5_HTML.gif , only for https://static-content.springer.com/image/art%3A10.1155%2FJIA%2F2006%2F48727/MediaObjects/13660_2005_Article_1604_IEq6_HTML.gif .
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Literature
1.
Alzer H: On some inequalities for the incomplete gamma function. Mathematics of Computation 1997,66(218):771–778. 10.1090/S0025-5718-97-00814-4MATHMathSciNetCrossRef
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/S1025583400000035MATHMathSciNet
3.
Gautschi W: Some elementary inequalities relating to the gamma and incomplete gamma function. Journal of Mathematics and Physics 1959, 38: 77–81.MATHMathSciNetCrossRef
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).MATHMathSciNet
5.
Qi F, Guo S-L: Inequalities for the incomplete gamma and related functions. Mathematical Inequalities & Applications 1999,2(1):47–53.MATHMathSciNetCrossRef
Metadata
Title
Supplements to known monotonicity results and inequalities for the gamma and incomplete gamma functions
Authors
A. Laforgia
P. Natalini
Publication date
01-12-2006
Publisher
Springer International Publishing
Published in
Journal of Inequalities and Applications / Issue 1/2006
Electronic ISSN: 1029-242X
DOI
https://doi.org/10.1155/JIA/2006/48727

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