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

DOI10.1016/j.cam.2014.03.004zbMath1293.33002arXiv1403.0278OpenAlexW2050668358MaRDI QIDQ396270

Feng Qi

Publication date: 8 August 2014

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1403.0278

zbMATH Keywords

gamma functionintegral representationremaindercomplete monotonicitylogarithmically completely monotonic functionBurnside's formula

Mathematics Subject Classification ID

Gamma, beta and polygamma functions (33B15) Monotonic functions, generalizations (26A48) Approximation by other special function classes (41A30) Remainders in approximation formulas (41A80)

Related Items (21)

A more accurate approximation for the gamma function ⋮ An accurate approximation formula for gamma function ⋮ Windschitl type approximation formulas for the gamma function ⋮ Approximations for certain hyperbolic functions by partial sums of their Taylor series and completely monotonic functions related to gamma function ⋮ Completely monotonic degree of a function involving trigamma and tetragamma functions ⋮ Some best approximation formulas and inequalities for the Wallis ratio ⋮ A family of Windschitl type approximations for gamma function ⋮ Improved approximation formulas and inequalities for the Wallis ratio ⋮ Monotonicity and inequalities for the gamma function ⋮ A LOGARITHMICALLY COMPLETELY MONOTONIC FUNCTION INVOLVING THE RATIO OF GAMMA FUNCTIONS ⋮ Some inequalities for the trigamma function in terms of the digamma function ⋮ Two asymptotic expansions for gamma function developed by Windschitl's formula ⋮ Asymptotic formulas for gamma function with applications ⋮ Sharp Smith's bounds for the gamma function ⋮ Integral representations and complete monotonicity of remainders of the binet and Stirling formulas for the gamma function ⋮ Some properties of the divided difference of psi and polygamma functions ⋮ Sharp approximation formulas and inequalities for the Wallis ratio by continued fraction ⋮ A ratio of finitely many gamma functions and its properties with applications ⋮ On complete monotonicity for several classes of functions related to ratios of gamma functions ⋮ Monotonicity properties and bounds involving the two-parameter generalized Grötzsch ring function ⋮ Monotonicity, convexity, and complete monotonicity of two functions related to the gamma function

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