Related papers: More supplements to a class of logarithmically com…

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 prove logarithmically complete monotonicity properties of certain ratios of the $k$-gamma function. As a consequence, we deduce some inequalities involving the $k$-gamma and $k$-trigamma functions.

The psi function $\psi(x)$ is defined by $\psi(x)=\frac{\Gamma'(x)}{\Gamma(x)}$ and $\psi^{(i)}(x)$ for $i\in\mathbb{N}$ denote polygamma functions, where $\Gamma(x)$ is the gamma function. In this paper, we prove that the function $$…

Motivated by existing results, we present some completely monotonic functions involving the polygamma functions.

We obtain necessary and sufficient conditions on a function in order that it be the Laplace transform of an absolutely monotonic function. Several closely related results are also given.

In the paper, the authors introduce a matrix-parametrized generalization of the multinomial probability mass function that involves a ratio of several multivariate gamma functions. They show the logarithmic complete monotonicity of this…

We prove some properties of completely monotonic functions and apply them to obtain results on gamma and $q$-gamma functions.

Motivated by open questions in the papers " Refinements and sharpenings of some double inequalities for bounding the gamma function" and "Complete monotonicity and monotonicity of two functions defined by two derivatives of a function…

We present some completely monotonic functions involving the $q$-gamma function that are inspired by their analogues involving the gamma function.

In this paper, we study some properties such as the monotonicity, logarithmically complete monotonicity, logarithmic convexity, and geometric convexity, of the combinations of gamma function and power function. The results we obtain…

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…

In the paper, the authors establish an inequality involving exponential functions and sums, introduce a ratio of many gamma functions, discuss properties, including monotonicity, logarithmic convexity, (logarithmically) complete…

In this paper, we present the necessary and sufficient conditions such that several functions involving $R\left( x\right) =\psi \left( x+1/2\right) -\ln x$ with a parameter are completely monotone on $\left( 0,\infty \right) $, where $\psi…

Motivated by several conjectures posed in the paper "F. Qi and A.-Q. Liu, Completely monotonic degrees for a difference between the logarithmic and psi functions, J. Comput. Appl. Math., vol. 361, pp. 366--371 (2019); available online at…

It is defined $\Gamma_{p,q}$ function, a generalize of $\Gamma$ function. Also, we defined $\psi_{p,q}$-analogue of the psi function as the log derivative of $\Gamma_{p,q}$. For the $\Gamma_{p,q}$ -function, are given some properties…

Let $ f:(0,\infty)\rightarrow \Bbb{R} $ be a completely monotonic function. In this paper, we present some properties of this functions and several new classes of completely monotonic functions. We also give some special functions such that…

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.

In the paper, the authors review origins, motivations, and generalizations of a series of inequalities involving several exponential functions and sums, establish three new inequalities involving finite exponential functions and sums by…

In this note we study the monotonicity of the function $x\mapsto \psi(1 +bx)^a/\psi(1 + ax)^b$. We also give the several inequalities involving the psi function, whic is the logarithmic derivative of the gamma function.

In the paper, we establish an inequality involving the gamma and digamma functions and use it to prove the negativity and monotonicity of a function involving the gamma and digamma functions.