derive the probability density function,the mathematical expectation expression,and variance of chi-square distributions,and to solve some problems of numerical characteristics of probability distributions.At the end,this paper summarizes the applications of gamma functions in probabilistic and statistical ...
Conditions for Convexity of a derivative and some applications to the Gamma function - Merkle - 1998 () Citation Context ...easy to show that condition (6.4) is implied by the condition that f ′′(x)→ 0 as x→ +∞. The rest follows from Theorem 6.3. 7 Equivalent Conditions for ...
Monotonicity and log-behavior of some functions related to the Euler Gamma function The aim of this paper is to develop analytic techniques to deal with the monotonicity of certain combinatorial sequences. On the one hand, a criterion for ... BX Zhu - 《Proceedings of the Edinburgh Mathematical...
Theory and Applications of Special Functions: On a generalized Gamma convolution related to the q-calculus We give short elementary proofs of a formula of Ramanujan as interpreted by Bradley, and a companion formula originally proved by W. Chu. We also give an e... C Berg,C Berg,C Berg ...
Euler's gamma function Γ(x) is logarithmically convex on (0, ∞). Additivity of logarithmic convexity implies that the function x→∑fkΓ(x+k) is also log... SI Kalmykov,DB Karp - 《Integral Transforms & Special Functions》 被引量: 18发表: 2013年 A Class of logarithmically completely ...
A general fixed point theorem for isometries in terms of metric functionals is proved under the assumption of the existence of a conical bicombing. It is n
Two representations of the extended gamma functions $\Gamma^{2,0}_{0,2}[(b,x)]$ are proved. These representations are exploited to find a transformation relation between two Fox's $H$-functions. These results are used to solve Fox's $H$-function in terms of Meijer's $G$-function ...
. then the local fractional integral of χ on \([\varkappa _{1},\varkappa _{2}]\) of order α̇ is defined by $$\begin{aligned} _{\varkappa _{1}}\mathcal{i}_{\varkappa _{2}}^{(\dot{\alpha })}\chi ( \epsilon ) =& \frac{1}{\gamma (1+\dot{\alpha })} \int ...
Coefficient of restitution \(\sigma_{k}\) and \(\sigma_{\epsilon }\) : Turbulent Prandtl numbers for \(k\) and \(\epsilon\) \({\Gamma }\) : Surface energy \(\epsilon_{ij}\) : Dissipation \(\delta_{adh}\) : Adhesive distance \(\tau_{f }\) : Viscous stress tensor ...
Let a and b be two real numbers and f be a positive and differentiable function on an interval I. The authors establish the i-log-convex or i-log-concave properties for i of the function [f(bx)] a /[f(ax)] b for axI and bxI when the function u k1[ln f(u)](k) for k is...