Related papers: Integral representations and complete monotonicity…
In this paper, we investigate the complete monotonicity of some functions involving gamma function. Using the monotonic properties of these functions, we derived some inequalities involving gamma and beta functions. Such inequalities…
In the paper, the authors concisely survey and review some functions involving the gamma function and its various ratios, simply state their logarithmically complete monotonicity and related results, and find necessary and sufficient…
In the paper, necessary and sufficient conditions are presented for a function involving a ratio of gamma functions to be logarithmically completely monotonic. This extends and generalizes the main result in [\emph{Inequalities and…
We present some completely monotonic functions involving the$q$-polygamma functions, our result generalizes some known results.
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 present some completely monotonic functions involving the $q$-gamma function that are inspired by their analogues involving the gamma function.
In this article, logarithmically complete monotonicity properties of some functions such as $\frac1{[\Gamma(x+1)]^{1/x}}$, $\frac{[{\Gamma(x+\alpha+1)}]^{1/(x+\alpha)}}{[{\Gamma(x+1)}]^{1/x}}$, $\frac{[\Gamma(x+1)]^{1/x}}{(x+1)^\alpha}$ and…
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…
By using Cauchy integral formula in the theory of complex functions, the authors establish some integral representations for the principal branches of several complex functions involving the logarithmic function, find some properties, such…
The monotonicity properties of remainder of Stirling's formula for the gamma function are simply obtained by using the integral transforms with series.
Motivated by existing results, we present some completely monotonic functions involving the polygamma functions.
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…
We simplify the proof of some widely used theoretical theorems, extending their applicability, while correcting some erroneous results. We also generalize key results and present new results that contribute to the development of the theory.…
In the paper, we present a monotonicity result of a function involving the gamma function and the logarithmic function, refine a double inequality for the gamma function, and improve some known results for bounding the gamma function.
We prove some properties of completely monotonic functions and apply them to obtain results on gamma and $q$-gamma functions.
In the paper, the authors discover an integral representation, some inequalities, and complete monotonicity of Bernoulli numbers of the second kind.
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.
In this expository and survey paper, along one of main lines of bounding the ratio of two gamma functions, we look back and analyse some inequalities, the complete monotonicity of several functions involving ratios of two gamma or $q$-gamma…
We investigate conditions for logarithmic complete monotonicity of product ratios of gamma and q-gamma functions whose arguments are linear functions of the variable. We give necessary and sufficient conditions in terms of nonnegativity of…
In this paper, the logarithmically complete monotonicity property for a functions involving $q$-gamma function is investigated for $q\in(0,1).$ As applications of this results, some new inequalities for the $q$-gamma function are…