Completely monotonic functions of positive order and asymptotic expansions of the logarithm of Barnes double gamma function and Euler's gamma function
From MaRDI portal
Publication:1018333
DOI10.1016/j.jmaa.2009.01.042zbMath1169.33001arXiv0811.2870OpenAlexW2081972949MaRDI QIDQ1018333
Stamatis Koumandos, Henrik Laurberg Pedersen
Publication date: 19 May 2009
Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/0811.2870
Gamma, beta and polygamma functions (33B15) Elementary classical functions (33B99) Monotonic functions, generalizations (26A48) Functions of one variable (26A99)
Related Items
A more accurate approximation for the gamma function, Complete characterizations of the gamma function, Completely monotonic degree of a function involving trigamma and tetragamma functions, Completely monotonic integer degrees for a class of special functions, Asymptotic expansions and inequalities relating to the gamma function, Inequalities and asymptotic expansions associated with the Ramanujan and nemes formulas for the gamma function, Multiple Gamma Functions and Their Applications, Asymptotic expansions for Barnes \(G\)-function, Series representations of the remainders in the expansions for certain functions with applications, On the Laplace transform of absolutely monotonic functions, Some exact constants for the approximation of the quantity in the Wallis' formula, Nielsen's beta function and some infinitely divisible distributions, Sharp inequalities and asymptotic expansions for the gamma function, Asymptotic expansions and complete monotonicity properties for the Barnes \(G\)-function, Functions operating on several multivariate distribution functions, Higher order Thorin-Bernstein functions, Asymptotic expansions for the Wallis sequence and some new mathematical constants associated with the Glaisher-Kinkelin and Choi-Srivastava constants, Inequalities, asymptotic expansions and completely monotonic functions related to the gamma function, Asymptotic formulas for the triple gamma function \(\varGamma _{3}\) by means of its integral representation, Pre Stieltjes functions, A LOGARITHMICALLY COMPLETELY MONOTONIC FUNCTION INVOLVING THE RATIO OF GAMMA FUNCTIONS, Some inequalities and monotonicity properties associated with the gamma and psi functions, Krull's theory for the double gamma function, Lévy-Khintchine representations of the weighted geometric mean and the logarithmic mean, Some inequalities for the trigamma function in terms of the digamma function, Monotonicity properties, inequalities and asymptotic expansions associated with the gamma function, Inequalities and asymptotic expansions related to the volume of the unit ball in \(\mathbb{R}^n\), A one-parameter family of Pick functions defined by the Gamma function and related to the volume of the unit ball in $n$-space, Turán type inequalities for the partial sums of the generating functions of Bernoulli and Euler numbers, More asymptotic expansions for the Barnes \(G\)-function, Asymptotic expansions for certain mathematical constants and special functions, Padé approximant related to Ramanujan's formula for the gamma function, Complete monotonicity and related properties of some special functions, Padé approximant related to asymptotics for the gamma function, Integral representations and complete monotonicity of remainders of the binet and Stirling formulas for the gamma function, Inequalities associated with Barnes \(G\)-function, Absolutely monotonic functions related to Euler's gamma function and Barnes' double and triple gamma function, THE BURNSIDE APPROXIMATION OF GAMMA FUNCTION, Some completely monotonic functions of positive order, Some properties of the divided difference of psi and polygamma functions, On a conjecture for trigonometric sums and starlike functions. II., Some properties of a sequence arising from geometric probability for pairs of hyperplanes intersecting with a convex body, Sharp inequalities involving \((n!)^{1/n}\), Some two-sided inequalities for multiple Gamma functions and related results, A note on complete monotonicity of the remainder in Stirling's formula, On complete monotonicity for several classes of functions related to ratios of gamma functions, Completely monotonic degrees for a difference between the logarithmic and psi functions, Qi's conjectures on completely monotonic degrees of remainders of asymptotic formulas of di- and trigamma functions, Generalized Stieltjes functions and their exact order, A class of strongly completely monotonic functions related to gamma function, Some properties of functions related to the gamma and psi functions, On asymptotic expansions of generalized Stieltjes functions, Some new properties of the Barnes G-function and related results, Bounds for completely monotonic degrees of remainders in asymptotic expansions of the digamma function
Cites Work
- Unnamed Item
- Uniform asymptotics for the incomplete gamma functions starting from negative values of the parameters
- Remarks on some completely monotonic functions
- The remainder in Ruijsenaars' asymptotic expansion of Barnes double gamma function
- Completely monotonic and related functions
- On Ruijsenaars' asymptotic expansion of the logarithm of the double gamma function
- On the remainder in an asymptotic expansion of the double gamma function
- Error Bounds for Asymptotic Expansions of the Ratio of Two Gamma Functions
- Superadditive Functions and a Statistical Application
- On some inequalities for the gamma and psi functions
- What is the Laplace Transform?
- On Barnes' multiple zeta and gamma functions
- An asymptotic expansion of the double gamma function
