Results 41 to 50 of about 226 (67)

Necessary and sufficient conditions for a class of functions and their reciprocals to be logarithmically completely monotonic

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  

Fourier Tauberian Theorems and Applications [PDF]

arXiv, 2000
The main aim of the paper is to present a general version of the Fourier Tauberian theorem for monotone functions. This result, together with Berezin's inequality, allows us to obtain a refined version the Li-Yau estimate for the counting function of the Dirichlet Laplacian which implies the Li-Yau estimate itself and, at the same time, the asymptotic ...
arxiv  

Convexity of ratios of the modified Bessel functions of the first kind with applications. [PDF]

Rev Mat Complut, 2022
Yang ZH, Tian JF.
europepmc   +1 more source

A Note on Generating Functions for Hausdorff Moment Sequences [PDF]

Proc. Amer. Math. Soc. 136, 3171-3176, 2008, 2008
For functions $f$ whose Taylor coefficients at the origin form a Hausdorff moment sequence we study the behaviour of $w(y):=|f(\gamma+iy)|$ for $y>0$ ($\gamma\leq1$ fixed).
arxiv  

Some properties of the psi and polygamma functions [PDF]

Bai-Ni Guo and Feng Qi, Some properties of the psi and polygamma functions, Hacettepe Journal of Mathematics and Statistics 39 (2010), no. 2, 219--231, 2009
In this paper, some monotonicity and concavity results of several functions involving the psi and polygamma functions are proved, and then some known inequalities are extended and generalized.
arxiv  

Hypergeometric functions as generalized Stieltjes transforms [PDF]

arXiv, 2011
In this paper we apply generalized Stieltjes transform representation to study the generalized hypergeometric function. Among the results thus proved are new integral representations, inequalities, properties of the Pad\'{e} table and the properties of the generalized hypergeometric function as a conformal map.
arxiv  

Two sharp inequalities for bounding the Seiffert mean by the arithmetic, centroidal, and contra-harmonic means [PDF]

Advanced Studies in Contemporary Mathematics (Kyungshang) 25 (2015), no. 4, 547--552, 2012
In the paper, the authors find the best possible constants appeared in two inequalities for bounding the Seiffert mean by the linear combinations of the arithmetic, centroidal, and contra-harmonic means.
arxiv  

Equality of Ultradifferentiable Classes by Means of Indices of Mixed O-regular Variation. [PDF]

Results Math, 2022
Jiménez-Garrido J, Sanz J, Schindl G.
europepmc   +1 more source

A note on the main theorem for absolutely monotonic functions [PDF]

arXiv, 2012
We prove that the main theorem for absolutely monotonic functions from the book Mitrinovi\'{c}~D.S., Pe\v{c}ari\'{c}~J.E., Fink~A.M. "Classical And New Inequalities In Analysis", Kluwer Academic Publishers, 1993, is not valid without additional restrictions.
arxiv  

Notes on three conjectures involving the digamma and generalized digamma functions. [PDF]

J Inequal Appl, 2018
Matejíčka L.
europepmc   +1 more source