3,826 research outputs found
A Complete Monotonicity of the Gamma Function
The function 1/x ln Ī(x+1)āln x+1 is strictly completely monotonic
on (0,ā)
Logarithmically Completely Monotonic Ratios of Mean Values and an Application
In the article, some strictly Logarithmically completely monotonic
ratios of mean values are presented
Monotonicity and Inequalities for Ratio of the Generalized Logarithmic Means
Let c > b > a > 0 be real numbers. Then the function f(r) =
Lr(a,b)/Lr(a,c) is strictly decreasing on (āā,ā), where Lr(a, b) denotes the generalized (extended) logarithmic mean of two positive numbers a and b
On the asymptotics of products related to generalizations of the Wilf and Mortini problems
In this paper, we present the connection between generalized Wilfāsand Mortiniās problems. We also consider the connection betweenanother infinite product formula and limit relation with severalparameters
Inequalities and asymptotic expansions related to the volume of the unit ball in R<sup>n</sup>
LetĀ Ī©n=Ļn/2/Ī(n2+1)(nāN)Ī©n=Ļn/2/Ī(n2+1)(nāN)Ā denote the volume of the unit ball inĀ RnRn. In this paper, we present asymptotic expansions and inequalities related toĀ Ī©nĪ©nĀ and the quantities:Ī©nā1Ī©n,Ī©nĪ©nā1+Ī©n+1andĪ©1/nnĪ©1/(n+1)n+1
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