Related papers: Some two-parameter families of generalized Bernste…
In this paper we introduce the Two Parameter Gamma Function, Beta Function and Pochhammer Symbol. We named them, as p - k Gamma Function, p - k Beta Function and p - k Pochhammer Symbol and denoted as $_{p}\Gamma_{k}(x), $ $_{p}B_{k}(x,y) $…
In this paper, we continue studying the properties of $\gamma$-semi-continuous and $\gamma$-semi-open functions introduced in [5].
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.…
We improve the upper bounds of the following inequalities proved in [H. Alzer and N. Batir, Monotonicity properties of the gamma function, Appl. Math. Letters, 20(2007), 778-781]. \begin{equation*}…
In this paper, we define a q-adic factorial and we demonstrate some properties of a generalized p-adic gamma function. Also, some numerical examples have been given
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 describe the computation of generalized Green functions and 2-parameter Green functions for finite reductive groups.
In a recent survey, Schmidt compiled equivalences between generalized bent functions, group invariant Butson Hadamard matrices, and abelian splitting relative difference sets. We establish a broader network of equivalences by considering…
We introduce a family of regularized functionals $g_n(x)$ that generalize the Euler--Mascheroni constant $\gamma$. They arise from a weighted regularization of Clausen-type trigonometric sums, and admit explicit integral representations,…
We prove some properties of completely monotonic functions and apply them to obtain results on gamma and $q$-gamma functions.
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…
Inspired by a recent work of Mesnager, we present several new infinite families of quadratic ternary bent, near-bent and 2-plateaued functions from some known quadratic ternary bent functions. Meanwhile, the distribution of the Walsh…
In this paper, we extend recent work on the functions that we call Bernstein-gamma to the class of bivariate Bernstein-gamma functions. In the more general bivariate setting, we determine Stirling-type asymptotic bounds which generalise,…
Some elaborations regarding the Hilbert and Fourier transforms of Fermi function are presented. The main result shows that the Hilbert transform of the difference of two Fermi functions has an analytical expression in terms of the $\Psi$…
Based on the generalized Boltzmann equation and the reverse function of the distribution function, we investigate the two-parameter generalized statistics and get an expression between the two parameters (k,r) and the physical quantities…
Using a probabilistic approach, we derive some interesting combinatorial identities involving gamma and beta functions. These results generalize certain well-known combinatorial identities involving binomial coefficients and special…
We study the equation $M_\Psi(z+1)=\frac{-z}{\Psi(-z)}M_\Psi(z), M_\Psi(1)=1$ defined on a subset of the imaginary line and where $\Psi$ is a negative definite functions. Using the Wiener-Hopf method we solve this equation in a two terms…
We consider convexity and monotonicity properties for some functions related to the $q$-gamma function. As applications, we give a variety of inequalities for the $q$-gamma function, the $q$-digamma function $\psi_q(x)$, and the $q$-series.…
In this note we present a method for obtaining a wide class of combinatorial identities. We give several examples, in particular, based on the Gamma and Beta functions. Some of them have already been considered by previously, and other are…
The main aim of this paper is to provide a unified approach to deriving identities for the Bernstein polynomials using a novel generating function. We derive various functional equations and differential equations using this generating…