Related papers: The integrals in Gradshteyn and Ryzhik. Part 11: T…

The object of this paper is to investigate the certain results involving Bateman's matrix polynomials for integral index. We obtain some properties, integral representation and recurrence relations for hypergeometric matrix function. We…

This paper investigates the generalized beta-logarithmic matrix function (GBLMF),which combines the extended beta matrix function and the logarithmic mean. The study establishes essential properties of this function, including functional…

The non-elementary integrals $\mbox{Si}_{\beta,\alpha}=\int [\sin{(\lambda x^\beta)}/(\lambda x^\alpha)] dx,\beta\ge1,\alpha>\beta+1$ and $\mbox{Ci}_{\beta,\alpha}=\int [\cos{(\lambda x^\beta)}/(\lambda x^\alpha)] dx, \beta\ge1,…

Following and generalizing a construction by Kontsevich, we associate a zeta function to any matrix with entries in a ring of noncommutative Laurent polynomials with integer coefficients. We show that such a zeta function is an algebraic…

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…

Using elementary methods we find surprising connections between the values of the Riemann Zeta Function over integers and the fractional parts of rational powers, and a connection between the Riemann Zeta Function and the Prime Zeta…

Some special functions are particularly relevant in applied probability and statistics. For example, the incomplete beta function is the cumulative central beta distribution. In this paper, we consider the inversion of the central…

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…

We propose an ansatz for the nonperturbative beta function of a generic non-supersymmetric Yang-Mills theory with or without fermions in an arbitrary representation of the gauge group. While our construction is similar to the recently…

In this article, we define a special function called the Bigamma function. It provides a generalization of Euler's gamma function. Several algebraic properties of this new function are studied. In particular, results linking this new…

The basis functions of the Fourier interpolation formula of Radchenko and Viazovska, constructed by means of weakly holomorphic modular forms for the Hecke theta group, are entire functions of order $2$ having interesting time-frequency…

In this article, we present a new two-dimensional generalization of the gamma function based on the product of the one-dimensional generalized beta function and the one-dimensional generalized gamma function. As will become clear later,…

We consider the problem of determining the beta-functions for any reduced effective field theory. Even though not all the Green's functions of a reduced effective field theory are renormalizable, unlike the full effective field theory,…

We establish a new multiplicity lemma for solutions of a differential system extending Ramanujan's classical differential relations. This result can be useful in the study of arithmetic properties of values of Riemann zeta function at odd…

This is a compendium of generating functions involving single, double sums and definite integrals. These generating functions also involve special functions in both the summand function and closed form solution.

In this paper, we first introduce certain forms of extended incomplete Pochhammer symbols which are then used to define families of extended incomplete generalized hypergeometric functions. For these functions, we investigate various…

This article provides novel analytical results for the Rice function, the incomplete Toronto function and the incomplete Lipschitz-Hankel Integrals. Firstly, upper and lower bounds are derived for the Rice function, $Ie(k,x)$. Secondly,…

We present some explicit computations checking a particular form of gradient formula for a boundary beta function in two-dimensional quantum field theory on a disc. The form of the potential function and metric that we consider were…

We introduce iterated beta integrals, a new class of iterated integrals on the universal abelian covering of the punctured projective line that unifies hyperlogarithms and classical beta integrals while preserving their fundamental…

Inspired by certain interesting recent extensions of the gamma, beta and hypergeometric matrix functions, we introduce here new extension of the gamma and beta matrix function. We also introduce new extensions of the Gauss hypergeometric…