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An asymptotic expansion for a ratio of products of gamma functions [PDF]
Internat. J. Math. & Math. Sci., Vol. 24, No. 8 (2000) 505-510, 2000 An asymptotic expansion of a ratio of products of gamma functions is derived. It generalizes a formula which was stated by Dingle, first proved by Paris, and recently reconsidered by Olver.
Buehring, Wolfgang
arxiv +7 more sources
Asymptotic expansions for ratios of products of gamma functions [PDF]
International Journal of Mathematics and Mathematical Sciences, Volume 2003, Issue 18, Page 1167-1171, 2003., 2003 An asymptotic expansion for a ratio of products of gamma functions is derived.Comment: 6 pages. v2: A paragraph containing one additional reference included at the end.
Bühring, Wolfgang
core +5 more sources
Limit formulas for ratios of polygamma functions at their singularities [PDF]
Feng Qi, Limit formulas for ratios between derivatives of the
gamma and digamma functions at their singularities, Filomat 27 (2013), no. 4,
601--604, 2012 In the paper the author presents limit formulas for ratios of polygamma functions at their singularities.
Qi, Feng
arxiv +4 more sources
Integral representation of some functions related to the Gamma function [PDF]
arXiv, 2004 We prove that the functions Phi(x)=[Gamma(x+1)]^{1/x}(1+1/x)^x/x and log Phi(x) are Stieltjes transforms.
Berg, Christian
arxiv +3 more sources
New properties for the Ramanujan R-function
Open Mathematics, 2022 In the article, we establish some monotonicity and convexity (concavity) properties for certain combinations of polynomials and the Ramanujan R-function by use of the monotone form of L’Hôpital’s rule and present serval new asymptotically sharp bounds ...
Cai Chuan-Yu +3 more
doaj +1 more source
Increasing property and logarithmic convexity of functions involving Dirichlet lambda function
Demonstratio Mathematica, 2023 In this article, with the help of an integral representation of the Dirichlet lambda function, by means of a monotonicity rule for the ratio of two integrals with a parameter, and by virtue of complete monotonicity and another property of an elementary ...
Qi Feng, Lim Dongkyu
doaj +1 more source
Integral transforms involving a generalized k-Bessel function
Demonstratio Mathematica, 2023 The main goal of this study was to look into some new integral transformations that are associated with a generalized kk-Bessel function. Integral formulas for the generalized kk-Bessel function have been established using the Laplace transform, Euler ...
Khammash Ghazi S. +4 more
doaj +1 more source
Advanced Nonlinear Studies, 2021 The existence of at least one positive solution to a large class of both integer- and fractional-order nonlocal differential equations, of which one model case ...
Goodrich Christopher S.
doaj +1 more source
A combinatorial proof of the Gaussian product inequality beyond the MTP2 case
Dependence Modeling, 2022 A combinatorial proof of the Gaussian product inequality (GPI) is given under the assumption that each component of a centered Gaussian random vector X=(X1,…,Xd){\boldsymbol{X}}=\left({X}_{1},\ldots ,{X}_{d}) of arbitrary length can be written as a ...
Genest Christian, Ouimet Frédéric
doaj +1 more source
Binet's second formula, Hermite's generalization, and two related identities
Open Mathematics, 2023 Legendre was the first to evaluate two well-known integrals involving sines and exponentials. One of these integrals can be used to prove Binet’s second formula for the logarithm of the gamma function.
Boyack Rufus
doaj +1 more source