Related papers: Logarithmically Complete Monotonicity of Certain R…

We make some observation on the logarithmic version of K-stability.

The article considers the generalized k-Bessel functions and represents it as Wright functions. Then we study the monotonicity properties of the ratio of two different orders k- Bessel functions, and the ratio of the k-Bessel and the…

We prove a matrix trace inequality for completely monotone functions and for Bernstein functions. As special cases we obtain non-trivial trace inequalities for the power function x->x^q, which for certain values of q complement McCarthy's…

Let $\psi(x)$ be the di-gamma function, the logarithmic derivative of the classical Euler's gamma function $\Gamma(x)$. In the paper, the author shows that the completely monotonic degree of the function $[\psi'(x)]^2+\psi''(x)$ is $4$,…

In this paper, we present and prove some generalizations of some inequalities for the $p$-Gamma, $q$-Gamma and $k$-Gamma functions. Our approach makes use of the series representations of the psi, $p$-psi, $q$-psi and $k$-psi functions.

We investigate conditions for logarithmic complete monotonicity of a quotient of two products of gamma functions, where the argument of each gamma function has different scaling factor. We give necessary and sufficient conditions in terms…

This paper considers various integrals where the integrand includes the log gamma function (or its derivative, the digamma function) multiplied by a trigonometric or hyperbolic function. Some apparently new integrals and series are…

An elementary, but very useful lemma due to Biernacki and Krzy\.{z} (1955) asserts that the ratio of two power series inherits monotonicity from that of the sequence of ratios of their respective coefficients. Over the last two decades it…

We consider the value distribution of logarithms of symmetric power L-functions associated with newforms of even weight and prime power level. In the symmetric square case, under certain plausible analytical conditions, we prove that…

We consider the following question: if a function of the form $\int_0^{\infty}\varphi(t)\, e^{-xt}dt$ is completely monotonic, is it then $\varphi\ge0$? It turns out that the question is related to a moment problem. In the end we apply…

We mainly establish a monotonicity property between some special Riemann sums of a convex function $f$ on $[a,b]$, which in particular yields that $\frac{b-a}{n+1}\sum_{i=0}^n f\left(a+i\frac{b-a}{n}\right)$ is decreasing while…

This communication shows the track for finding a solution for a sin(kx)/k**2 series and a fresh representation for the Euler's Gamma function in terms of Riemann's Zeta function. We have found a new series expression for the logarithm as a…

In this paper we will give a proof of a certain summation formula for Gamma functions utilizing Gegenbauer polynomials.

In this paper we consider several families of potential non-isochronous systems and study their associated period functions. Firstly, we prove some properties of these functions, like their local behavior near the critical point or…

Complete monotonicity, Laguerre and Tur\'an type inequalities are established for the so-called Kr\"atzel function $Z_{\rho}^{\nu},$ defined by $$Z_{\rho}^{\nu}(u)=\int_0^{\infty}t^{\nu-1}e^{-t^{\rho}-\frac{u}{t}}\dt,$$ where $u>0$ and…

In this work we establish a connection between two classical notions, unrelated so far: Harmonic functions on the one hand and absolutely monotonic functions on the other hand. We use this to prove convexity type and propagation of…

We prove new monotonicity properties for joint and generalized spectral radius and their essential versions of weighted geometric symmetrizations of bounded sets of positive kernel operators on $L^2$. To our knowledge, several proved…

In this paper, we investigate the monotone property of the continued fractions $G(m,\lambda)$ as a function of $m$ and $\lambda$. In particular, we obtain new inequality for the relative continued fractions.

We characterize the complete monotonicity of the Kilbas-Saigo function on the negative half-line. We also provide the exact asymptotics at $-\infty$, and uniform hyperbolic bounds are derived. The same questions are addressed for the…

We introduce completely monotonic functions of order $r>0$ and show that the remainders in asymptotic expansions of the logarithm of Barnes double gamma function and Euler's gamma function give rise to completely monotonic functions of any…