Journal ArticleDOI
Integral representation of some functions related to the Gamma function
TLDR
In this paper, it was shown that the functions Θ(Θ(x) = [Gamma (x + 1)]^{1/x} (1 + 1/x)^x /x) and Θ (Θ (x, Θ) = Θ((Θ + 1)/x)) are Stieltjes transforms.Citations
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Logarithmically complete monotonicity of a matrix-parametrized analogue of the multinomial distribution
Frédéric Ouimet,Feng Qi +1 more
TL;DR: In this article, a matrix-parametrized generalization of the multinomial probability mass function that involves a ratio of several multivariate gamma functions is introduced. And the authors show the logarithmically complete monotonicity of this generalization and derive new inequalities involving ratios of multivariate Gamma functions.
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Logarithmically completely monotontic functions related the $q-$gamma and the $q-$digamma functions with applications
TL;DR: In this article, Chen and Qi presented several new classes of logarithmically completely monotonic functions, which are defined in terms of the $q-$gamma and $q-digamma functions.
Journal ArticleDOI
Logarithmically complete monotonicity of ratios of q-gamma functions
TL;DR: In this article , the necessary and sufficient conditions for the ratio Wq;u,v/Wq;r,s to be logarithmically completely monotonic on (−ρ,∞) were presented.
Journal ArticleDOI
Affine relation between an infinitely divisible distribution function and its Lévy measure
TL;DR: In this paper, the Kendall-Ressel law is characterized in terms of an affine relation linking the probability masses with those of its jump law and the continuous version of this relation leads to the so-called Geeta laws.
References
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Book
Table of Integrals, Series, and Products
TL;DR: Combinations involving trigonometric and hyperbolic functions and power 5 Indefinite Integrals of Special Functions 6 Definite Integral Integral Functions 7.Associated Legendre Functions 8 Special Functions 9 Hypergeometric Functions 10 Vector Field Theory 11 Algebraic Inequalities 12 Integral Inequality 13 Matrices and related results 14 Determinants 15 Norms 16 Ordinary differential equations 17 Fourier, Laplace, and Mellin Transforms 18 The z-transform
A table of integrals
TL;DR: Basic Forms x n dx = 1 n + 1 x n+1 (1) 1 x dx = ln |x| (2) udv = uv − vdu (3) 1 ax + bdx = 1 a ln|ax + b| (4) Integrals of Rational Functions