Sharp bounds for gamma and digamma function arising from Burnside's formula

Cristinel Mortici

doi:10.33993/jnaat391-920

Authors

Cristinel Mortici Valahia University of Târgovişte, Romania

DOI:

https://doi.org/10.33993/jnaat391-920

Keywords:

factorial \(n\), Stirling's formula, Burnside's formula, complete monotonicity, Euler-Mascheroni constant, sharp inequalities

Abstract views: 200

Abstract

The main aim of this paper is to improve the Burnside's formula for approximating the factorial function. We prove the complete monotonicity of a function involving the gamma function to establish new lower and upper sharp bounds for the gamma and digamma function.

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References

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