Results 1 to 10 of about 92 (86)
Some New Application of Extended Wright Function
Abstract and Applied AnalysisMSC2020 Classification: 26A33, 33B15, 33C05, 65D20, 33E20 ...
Pallavi Sharma +3 more
doaj +3 more sources
Necessary and sufficient conditions for a class of functions and their reciprocals to be logarithmically completely monotonic [PDF]
Journal of Inequalities and Applications, 2011 We prove that the function F α,β (x) = x α Γ β (x)/Γ(βx) is strictly logarithmically completely monotonic on (0, ∞) if and only if (α, β) ∈ {(α, β) : β > 0, β ≥ 2 ...
Lv Yu-Pei, Sun Tian-Chuan, Chu Yu-Ming
doaj +3 more sources
Umbral Methods and Harmonic Numbers
Axioms, 2018 The theory of harmonic-based functions is discussed here within the framework of umbral operational methods. We derive a number of results based on elementary notions relying on the properties of Gaussian integrals.
Giuseppe Dattoli +2 more
exaly +3 more sources
Inequalities of extended beta and extended hypergeometric functions. [PDF]
J Inequal Appl, 2017 We study the log-convexity of the extended beta functions. As a consequence, we establish Tur\ue1n-type inequalities. The monotonicity, log-convexity, log-concavity of extended hypergeometric functions are deduced by using the inequalities on extended ...
Mondal SR.
europepmc +2 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
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
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
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
On generalized fractional integral with multivariate Mittag-Leffler function and its applications
Alexandria Engineering Journal, 2022 The fractional calculus (FC) has been extensively studied by researchers due to its vast applications in sciences in the last few years. In fractional calculus, multivariate Mittag–Leffler functions are considered the powerful extension of the classical ...
Amna Nazir +6 more
doaj +1 more source