Related papers: The Inverse of the Complex Gamma Function
Euler's Gamma function $\Gamma$ either increases or decreases on intervals between two consequtive critical points. The inverse of $\Gamma$ on intervals of increase is shown to have an extension to a Pick-function and similar results are…
In this paper we examine the existence of bicomplexified inverse Fourier transform as an extension of its complexified inverse version within the region of convergence of bicomplex Fourier transform. In this paper we use the idempotent…
The purpose of this note is to compare various approximation methods as applied to the inverse of the Bessel function of the first kind, in a given domain of the complex plane.
Inversion of function sinc(x) is studied. New series and integral representations of branches of inverse function are obtained using Fourier analysis.
This paper establishes a real integral representation of the reciprocal $\Gamma$ function in terms of a regularized hypersingular integral. The equivalence with the usual complex representation is demonstrated. A regularized complex…
Recently, extensions of gamma and beta functions have been studied by many researchers due to their nice properties and variety of applications in different fields of science. The aim of this note is to investigate generalized inequalities…
In this paper we examine the existence of bicomplexied inverse Laplacetransform as an extension of its complexied inverse version within theregion of convergence of bicomplex Laplace transform. In this course weuse the idempotent…
In this paper, we present some double inequalities involving certain ratios of the Gamma function. These results are further generalizations of several previous results. The approach is based on the monotonicity properties of some functions…
This paper continues a series of investigations on converging representations for the Riemann Zeta function. We generalize some identities which involve Riemann's zeta function, and moreover we give new series and integrals for the zeta…
In this paper we deal with some open problems concerned with gamma subordinators. In particular, we provide a representation for the moments of the inverse gamma subordinator. Then, we focus on $\lambda$-potentials and we study the…
We derive product and series representations of the gamma function using Newton interpolation series. Using these identities, a new formula for the coefficients in the Taylor series of the reciprocal gamma function is found. We also find…
The $\beta\gamma$ system is generalized by complex(rational) powers of the fields, which leads to a corresponding extension on the Fock space. Two different approaches to compute the Green functions of the physical operators are proposed.…
In this paper, we introduce a new two-parameter deformation of the Gamma function that generalizes some existing Gamma-type functions in the literature. We study properties of this function that depend on the parameters. We also prove some…
The present research deals with generalizations of the Salem function with arguments defined in terms of certain alternating expansions of real numbers. The special attention is given to modelling such functions by systems of functional…
In this note we explore the relationship between the operation of convolution of functions and the Eulerian integrals. This approach allow us to obtain some expressions for the convolution of a certain class of functions in terms of the…
This note deals with the direct and inverse spectral analysis for a class of infinite band symmetric matrices. This class corresponds to operators arising from difference quations with usual and inner boundary conditions. We give a…
The Implicit and Inverse Function Theorems are special cases of a general Implicit/Inverse Function Theorem which can be easily derived from either theorem. The theorems can thus be easily deduced from each other via the generalized…
We investigate the subclass of reversible functions that are self-inverse and relate them to reversible circuits that are equal to their reverse circuit, which are called palindromic circuits. We precisely determine which self-inverse…
This article handles in a short manner a few Laplace transform pairs and some extensions to the basic equations are developed. They can be applied to a wide variety of functions in order to find the Laplace transform or its inverse when…
In this paper, the authors establish some inequalities involving the $q$-extension of the classical Gamma function. These inequalities provide bounds for certain ratios of the $q$-extended Gamma function. The procedure makes use of…