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

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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References

  1. 1.

    Alzer H: On some inequalities for the incomplete gamma function. Mathematics of Computation 1997,66(218):771–778. 10.1090/S0025-5718-97-00814-4

    MATH  MathSciNet  Article  Google Scholar 

  2. 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/S1025583400000035

    MATH  MathSciNet  Google Scholar 

  3. 3.

    Gautschi W: Some elementary inequalities relating to the gamma and incomplete gamma function. Journal of Mathematics and Physics 1959, 38: 77–81.

    MATH  MathSciNet  Article  Google Scholar 

  4. 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).

    MATH  MathSciNet  Google Scholar 

  5. 5.

    Qi F, Guo S-L: Inequalities for the incomplete gamma and related functions. Mathematical Inequalities & Applications 1999,2(1):47–53.

    MATH  MathSciNet  Article  Google Scholar 

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Correspondence to A. Laforgia.

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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

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Keywords

  • Gamma Function
  • Incomplete Gamma Function
  • Monotonicity Result
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