Related papers: Higher order Thorin-Bernstein Functions
In this paper, we give the matrix version of Horn's hypergeometric function and its confluent cases. We also discuss the regions of convergence, the system of matrix differential equations of bilateral type, differential formulae and…
We describe a uniform way of obtaining basic hypergeometric functions as limits of the elliptic beta integral. This description gives rise to the construction of a polytope with a different basic hypergeometric function attached to each…
The main object of this paper is to present a new generalized beta function which defined by three parametres Mittag-Leffler function. We also introduce new generalizations of hypergeometric and confluent hypergeometric functions with the…
This is the second part of a work dedicated to the study of Bernstein-Sato polynomials for several analytic functions depending on parameters. In this part, we give constructive results generalizing previous ones obtained by the author in…
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…
A Fourier-type integral representation for Bessel's function of the first kind and complex order is obtained by using the Gegenbuaer extension of Poisson's integral representation for the Bessel function along with a trigonometric integral…
We describe a new approach to the notion of general hypergeometric functions
On the one hand the Fermi-Dirac and Bose-Einstein functions have been extended in such a way that they are closely related to the Riemann and other zeta functions. On the other hand the Fourier transform representation of the gamma and…
The authors survey recent results in special functions, particularly the gamma function and the Gaussian hypergeometric function.
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…
The primary goal of this paper is to introduce and investigate generalized incomplete exponential functions with matrix parameters. Integral representation, differential formula, addition formula, multiplication formula, and recurrence…
The report studies the generation of ternary bent functions by permuting the circular Vilenkin_Chrestenson spectrum of a known bent function. We call this spectral invariant operations in the spectral domain, in analogy to the spectral…
In this very short note we will derive an inequality for a class of entire functions including all the confluent basic hypergeometric series and an inequality for a class of meromorphic functions including theta functions.
This note introduces a new range of modified gamma and beta $k$ functions. The authors present new modified gamma and beta $k$-functions, first and second summation relations, various functionals, Mellin transforms, and integral…
Our purpose in this present paper is to investigate generalized integration formulas containing the extended generalized hypergeometric function and obtained results are expressed in terms of extended hypergeometric function. Certain…
We give a brief review of the main results of the theory of elliptic hypergeometric functions -- a new class of special functions of mathematical physics. We prove the most general univariate exact integration formula generalizing Euler's…
In this paper, we introduce and investigate a new extension of the beta function by means of an integral operator involving a product of Bessel-Struve kernel functions. We also define a new extension of the well-known beta distribution, the…
Generalized Bargmann representations which are based on generalized coherent states are considered. The growth of the corresponding analytic functions in the complex plane is studied. Results about the overcompleteness or undercompleteness…
Generalised definitions of exponential, trigonometric sine and cosine and hyperbolic sine and cosine functions are given. In the lowest order, these functions correspond to ordinary exponential, trigonometric sine etc. Some of the…
We introduce new generalizations of the Gamma and the Beta functions. Their properties are investigated and known results are obtained as particular cases.