Results 11 to 20 of about 681 (108)
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
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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
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A Complete Monotonicity of the Gamma Function [PDF]
, 2004 The function 1/x ln Γ(x+1)−ln x+1 is strictly completely monotonic on (0,∞)
Chen, Chao-Ping, Qi, Feng
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q-Functions and Distributions, Operational and Umbral Methods
Mathematics, 2021 The use of non-standard calculus means have been proven to be extremely powerful for studying old and new properties of special functions and polynomials.
Giuseppe Dattoli +3 more
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Monotonicity of Some Functions Involving The Beta Function [PDF]
Al-Rafidain Journal of Computer Sciences and Mathematics, 2011 In this short paper the monotonicity of functions involving the Beta function is considered to be study by using a similar method given in [2] and [4].
Hanadi Saleem
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A STUDY OF EXTENDED BETA, GAUSS AND CONFLUENT HYPERGEOMETRIC FUNCTIONS
, 2020 In the present research note, we define a new extension of beta function by making use of the multi-index Mittag-Leffler function. Here, first we derive its fundamental properties and then we present a new type of beta distribution as an application of ...
M. Ghayasuddin, N. Khan, M. Ali
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Generalization of Some Inequalities for the Ratio of Gamma Functions [PDF]
, 2014 access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Copyright C K. Nantomah +4 more
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A monotonicity property involving the generalized elliptic integral of the first kind
, 2017 In this paper, we prove that the function r → Y (r) = Ka(r) sin(πa)r′2 log(eR(a)/2/r′) − 1 r′2 is strictly increasing from (0,1) onto (π/[R(a)sin(πa)]−1,a(1−a)) for all a∈ (0,1/2] , where r′ = √ 1− r2 , Ka(r) is the generalized elliptic integral of the ...
Zhen-Hang Yang, Y. Chu
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International Journal of Mathematics and Mathematical Sciences, Volume 2004, Issue 39, Page 2091-2096, 2004., 2004 We present a Fourier transform representation of the gamma functions, which leads naturally to a distributional representation for them. Both of these representations lead to new identities for the integrals of gamma functions multiplied by other functions, which are also presented here.
M. Aslam Chaudhry, Asghar Qadir
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Hilbert-type inequalities involving differential operators, the best constants, and applications
, 2015 Motivated by some recent results, in this article we derive several Hilbert-type inequalities with a differential operator, regarding a general homogeneous kernel.
V. Adiyasuren +2 more
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