Related papers: On a new result for the hypergeometric function

We aim to achieve the following three goals. First of all, we collect all known definitions, transformation properties and functional identities of Barnes double gamma function $G(z;\tau)$. Second, we derive an algorithm for numerically…

Using a probabilistic approach, we derive several interesting identities involving beta functions. Our results generalize certain well-known combinatorial identities involving binomial coefficients and gamma functions.

From the algebraic solution of $x^{n}-x+t=0$ for $n=2,3,4$ and the corresponding solution in terms of hypergeometric functions, we obtain a set of reduction formulas for hypergeometric functions. By differentiation and integration of these…

In this paper, we aim to obtain a representation of Humbert's hy- pergeometric function in a series of Gauss's function 2F1. A few interesting results have also been deduced as special case of our main findings.

This note establishes several integral identities relating certain metric properties of level hypersurfaces of Morse functions.

In these lecture notes I give an elementary introduction to elliptic hypergeometric functions. I focus on motivating the main ideas and constructions, rather than giving a comprehensive survey. The lectures include a brief explanation of…

We begin by defining general hypergeometric functions over finite fields and obtaining a finite field analogue of a classical symmetry in their complex counterparts. We give a geometric proof for the symmetry by constructing isomorphisms…

In our previous work, a unified description as polynomial Hamiltonian systems was established for a broad class of the Schlesinger systems including the sixth Painleve equation and Garnier systems. The main purpose of this paper is to…

The authors survey recent results in special functions, particularly the gamma function and the Gaussian hypergeometric function.

The paper aims to generalize Clausen's identity to the square of any Gauss hypergeometric function. Accordingly, solutions of the related 3rd order linear differential equation are found in terms of certain bivariate series that can reduce…

A method to calculate exact Green's functions on lattices in various dimensions is presented. Expressions in terms of generalized hypergeometric functions in one or more variables are obtained for various examples by relating the resolvent…

This paper deals with the evaluation of some definite Euler-type integrals in terms of the Wright hypergeometric function. We obtain a theorem on the Wright hypergeometric function and then use this theorem to evaluate some definite…

Survey of hypergeometric motives, with a focus on their source varieties, Hodge numbers, and L-functions.

Adaptive dimensionality reduction in high-dimensional problems is a key topic in statistics. The multiplicative gamma process takes a relevant step in this direction, but improved studies on its properties are required to ease…

The main aim of this paper is to give a new generalization of Hurwitz-Lerch Zeta function of two variables.Also, we investigate several interesting properties such as integral representations, summation formula and a connection with…

The main aim of this paper is to provide a novel approach to deriving identities for the Bernstein polynomials using functional equations. We derive various functional equations and differential equations using generating functions.…

Recently, there emerges different versions of beta function and hypergeometric functions containing extra parameters. Gaining enlightenment from these ideas, we will first introduce a new extension of generalized hypergeometric function and…

Identities between Whittaker and modified Bessel functions are derived for particular complex orders. Certain polynomials appear in such identities, which satisfy a fourth order differential equation (not of hypergeometric type), and they…

In our recent work we proposed a generalization of the beta integral method for derivation of the hypergeometric identities which can by analogy be termed "the G function integral method". In this paper we apply this technique to the cubic…

The main purpose of this note is to provide a topological approach to defining additive functions on Riemannian co-compact normal coverings.