Related papers: Dihedral Gauss hypergeometric functions

We consider some hypergeometric functions and prove that they are elementary functions. Consequently, the second order moments of Meyer-Konig and Zeller type operators are elementary functions. The higher order moments of these operators…

Integral representations of hypergeometric functions proved to be a very useful tool for studying their properties. The purpose of this paper is twofold. First, we extend the known representations to arbitrary values of the parameters and…

One of the goals of the present paper is to propose an elementary method to find a general formula for the Fourier transform containing a pair of complex gamma functions with a monomial sm in terms of Gauss's hypergeometric functions 2F1.…

We review Aomoto's generalized hypergeometric functions on Grassmannian spaces Gr(k +1, n+1). Particularly, we clarify integral representations of the generalized hypergeometric functions in terms of twisted homology and cohomology. With an…

We principally present reductions of certain generalized hypergeometric functions $_3F_2(\pm 1)$ in terms of products of elementary functions. Most of these results have been known for some time, but one of the methods, wherein we…

We define the adelic hypergeometric function of special Gaussian type by means of a tower of hypergeometric curves. This function takes values in an adelic completed group ring and interpolates all the hypergeometric functions of the same…

This paper presents a somewhat exhaustive study on the conformable fractional Gauss hypergeometric function (CFGHF). We start by solving the conformable fractional Gauss hypergeometric equation (CFGHE) about the fractional regular singular…

This paper shows that certain $\,_{3}F_{4}$ hypergeometric functions may be expanded in sums of pair products of $\,_{2}F_{3}$ functions. This expands the class of hypergeometric functions having summation theorems beyond those expressible…

Several integrals involving powers and ordinary hypergeometric functions are rederived by means of a generalized hypergeometric function of two variables (Appell's function) recovering some well-known expressions as particular cases. Simple…

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…

Let G be the group of points of a quasi-split reductive algebraic group over a local field F. It follows from the local Langlands conjectures that to every non-trivial additive character of F and every representation of the Langlands dual…

In this note, we firstly establish an extended Gauss's summation identity. Using this identity, we compute values of a family of $_4F_3$ hypergeometric functions, which generalize the results obtained by Ferretti et al..

We introduce a natural method of computing antiderivatives of a large class of functions which stems from the observation that the series expansion of an antiderivative differs from the series expansion of the corresponding integrand by…

This article gives a classification scheme of algebraic transformations of Gauss hypergeometric functions, or pull-back transformations between hypergeometric differential equations. The classification recovers the classical transformations…

Present and future high-precision tests of the Standard Model and beyond for the fundamental constituents and interactions in Nature are demanding complex perturbative calculations involving multi-leg and multi-loop Feynman diagrams.…

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…

The relationship between Feynman diagrams and hypergeometric functions is discussed. Special attention is devoted to existing techniques for the construction of the $\epsilon$-expansion. As an example, we present a detailed discussion of…

We consider the isotropic perimeter generating functions of three-choice, imperfect, and 1-punctured staircase polygons, whose 8th order linear Fuchsian ODEs are previously known. We derive simple relationships between the three generating…

The classical quadratic Gauss sum can be thought of as an exponential sum attached to a quadratic form on a cyclic group. We introduce an equivariant version of Gauss sum for arbitrary finite quadratic forms, which is an exponential sum…

We study the group of transformations of 4F3 hypergeometric functions evaluated at unity with one unit shift in parameters. We reveal the general form of this family of transformations and its group property. Next, we use explicitly known…