Related papers: Some new inequalities for the gamma function
In this paper, the authors establish some inequalities involving the Psi and $k$-Gamma functions. The procedure utilizes some monotonicity properties of some functions associated with the Psi and $k$-Gamma functions.
In this paper we investigate the monotonicity properties related to the ratio of gamma functions, from which some related asymptotics and inequalities are established. Some special cases also confirm the conjectures of C.-P. Chen…
Recently, many researchers devoted their attention to study the extensions of the gamma and beta functions. In the present work, we focus on investigating some approximations for a class of Gauss hypergeometric functions by exploiting…
We discuss the best methods available for computing the gamma function $\Gamma(z)$ in arbitrary-precision arithmetic with rigorous error bounds. We address different cases: rational, algebraic, real or complex arguments; large or small…
In this paper we obtain some essential generalizations of certain Ramachandra's inequality, i. e. we obtain new lower estimates for the energies of some complicated signals generated by the Riemann zeta-function on the critical line.
In the paper, by using Lupa\c{s} integral inequality, the authors find some new inequalities for the complete elliptic integrals of the first and second kinds. These results improve some known inequalities.
We generalize the well-known mean value inequality of subharmonic functions for a slightly more general function class. We also apply this generalized mean value inequality to weighted boundary behavior and nonintegrability questions of…
In the paper, the authors introduce a notion "$(\alpha,m)$-GA-convex functions" and establish some integral inequalities of Hermite-Hadamard type for $(\alpha,m)$-GA-convex functions.
A $q$-analogue of the multiple gamma functions is introduced, and is shown to satisfy the generalized Bohr-Morellup theorem. Furthermore we give some expressions of these function.
In this paper, we establish (presumably new type) integral inequalities for convex functions via the Hermite--Hadamard's inequalities. As applications, we apply these new inequalities to construct inequalities involving special means of…
For a family of infinite-dimensional diffusions with degenerate noise, we develop a modified $\Gamma$ calculus on finite-dimensional projections of the equation in order to produce explicit functional inequalities that can be scaled to…
In this study, we obtain some new integral inequalities for different classes of convex functions by using some elementary inequalities and classical inequalities like general Cauchy inequality and Minkowski inequality.
In this paper, we establish some new Hadamard type inequalities using elementary well known inequalities for functions whose inequalities absolute values are {\alpha}-, m-, ({\alpha},m)-logarithmically convex.
Certain new inequalities for the sums of factorials are presented.
In the paper, some lower bounds for polygamma functions are refined.
In this paper, the versions of trigonometric functions of certain known inequalities for hyperbolic ones are proved, and then corresponding inequalities for means are presented.
We improve the upper bound of the following inequalities for the gamma function $\Gamma$ due to H. Alzer and the author. \begin{equation*}…
Some inequalities for the ratios of generalized digamma functions are presented. The approache makes use of the series representations of the $(q,k)$-digamma and $(p,q)$-digamma functions.
This paper presents invariants under gamma correction and similarity transformations. The invariants are local features based on differentials which are implemented using derivatives of the Gaussian. The use of the proposed invariant…
In this paper we established new integral inequalities which are more general results for coordinated convex functions on the coordinates by using some classical inequalities.