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Supplements to known monotonicity results and inequalities for the gamma and incomplete gamma functions
Journal of Inequalities and Applications volume 2006, Article number: 48727 (2006)
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.
Alzer H: On some inequalities for the incomplete gamma function. Mathematics of Computation 1997,66(218):771–778. 10.1090/S0025-5718-97-00814-4
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/S1025583400000035
Gautschi W: Some elementary inequalities relating to the gamma and incomplete gamma function. Journal of Mathematics and Physics 1959, 38: 77–81.
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).
Qi F, Guo S-L: Inequalities for the incomplete gamma and related functions. Mathematical Inequalities & Applications 1999,2(1):47–53.
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Laforgia, A., Natalini, P. Supplements to known monotonicity results and inequalities for the gamma and incomplete gamma functions. J Inequal Appl 2006, 48727 (2006). https://doi.org/10.1155/JIA/2006/48727
- Gamma Function
- Incomplete Gamma Function
- Monotonicity Result