Integral representations and complete monotonicity related to the remainder of Burnside's formula for the gamma function

Abstract

In the paper, the authors establish integral representations of some functions related to the remainder of Burnside's formula for the gamma function and find the (logarithmically) complete monotonicity of these and related functions. These results extend and generalize some known conclusions.

arXiv comment15 pages

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Cited by in corpus (10)

• A logarithmically completely monotonic function involving the ratio of gamma functions
• Some best approximation formulas and inequalities for Wallis ratio
• Completely monotonic degree of a function involving the tri- and tetra-gamma functions
• A ratio of many gamma functions and its properties with applications
• Some inequalities for the trigamma function in terms of the digamma function
• Some new inequalities for the gamma function
• Approximation and bounds for the Wallis ratio
• Asymptotic formulas for the gamma function constructed by bivariate means
• An accurate approximation formula for gamma function
• Two asymptotic expansions for gamma function developed by Windschitl's formula