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2011•Integral Transforms and Special FunctionsRequires access

Some completely monotonic functions relating to the gamma function

Cristinel Mortici

Open publisher page 4 citations

Abstract

We propose a new sharp family of approximations which improve the results of Sandor and Debnath [On certain inequalities involving the constant e and their applications, J. Math. Anal. Appl. 249 (2000), pp. 569–582], Batir [Sharp inequalities for factorial n, Proyecciones 27 (2008), pp. 97–102] and other recent results. Then, we prove the complete monotonicity of a function involving the gamma function to establish new sharp upper and lower bounds for the gamma and the digamma functions.

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What this paper is about

We propose a new sharp family of approximations which improve the results of Sandor and Debnath [On certain inequalities involving the constant e and their applications, J. Math. Anal. Appl. 249 (2000), pp. 569–582], Batir [Sharp inequalities for factorial n, Proyecciones 27 (2008), pp. 97–102] and other recent results. Then, we prove the complete monotonicity of a function involving the gamma function to establish new sharp upper and lower bounds for the gamma and the digamma functions.

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Available abstract

We propose a new sharp family of approximations which improve the results of Sandor and Debnath [On certain inequalities involving the constant e and their applications, J. Math. Anal. Appl. 249 (2000), pp. 569–582], Batir [Sharp inequalities for factorial n, Proyecciones 27 (2008), pp. 97–102] and other recent results. Then, we prove the complete monotonicity of a function involving the gamma function to establish new sharp upper and lower bounds for the gamma and the digamma functions.

Key concepts: Monotonic function, Mathematics, Digamma function, Gamma function, Factorial, Pure mathematics, Function (biology), Inequality

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