Related papers: HYPERgeometric functions DIfferential REduction: M…
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…
We present the Mathematica package HypExp which allows to expand hypergeometric functions $_JF_{J-1}$ around integer parameters to arbitrary order. At this, we apply two methods, the first one being based on an integral representation, the…
It is possible to perform some operations with extrafunctions applying these operations separately to each coordinate. Operations performed in this manner are called regular. It is proved that it is possible to extend several operations…
Finite hypergeometric functions are functions of a finite field ${\bf F}_q$ to ${\bf C}$. They arise as Fourier expansions of certain twisted exponential sums and were introduced independently by John Greene and Nick Katz in the 1980's.…
Sparse representation with training-based dictionary has been shown successful on super resolution(SR) but still have some limitations. Based on the idea of making the magnification of function curve without losing its fidelity, we proposed…
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…
An analysis of high-dimensional data can offer a detailed description of a system but is often challenged by the curse of dimensionality. General dimensionality reduction techniques can alleviate such difficulty by extracting a few…
We propose a framework for performing differentiable geometric modeling based on the Function Representation (FRep). The framework is built on top of modern libraries for performing automatic differentiation allowing us to obtain…
Sleeve functions are generalizations of the well-established ridge functions that play a major role in the theory of partial differential equation, medical imaging, statistics, and neural networks. Where ridge functions are non-linear,…
Using Mellin-Barnes integrals we give a method to compute a relevant subgroup of the monodromy group of an A-hypergeometric system of differential equations. Presumably this group is the full monodromy group of the system. This article is a…
Multivariate hypergeometric functions associated with toric varieties were introduced by Gel'fand, Kapranov and Zelevinsky. Singularities of such functions are discriminants, that is, divisors projectively dual to torus orbit closures. We…
We aim to introduce a new extension of beta function and to study its important properties. Using this definition, we introduce and investigate new extended hypergeometric and confluent hypergeometric functions. Further, some hybrid…
Humbert confluent hypergeometric functions of two variables arise in many problems of mathematical physics and applied analysis, yet their behavior with respect to parameters has not been systematically studied. In this paper we investigate…
The A-hypergeometric system studied by I.M. Gelfand, M.I. Graev, A.V. Zelevinsky and the author, is defined for a set A of characters of an algebraic torus. In this paper we propose a generalization of the theory where the torus is replaced…
We present the Olsson$.$wl Mathematica package which aims to find linear transformations for some classes of multivariable hypergeometric functions. It is based on a well-known method developed by P. O. M. Olsson in J. Math. Phys. 5, 420…
Multivariate functions encountered in high-dimensional uncertainty quantification problems often vary most strongly along a few dominant directions in the input parameter space. We propose a gradient-based method for detecting these…
In this work, generalized hypergeometric functions for bicomplex argument is introduced and its convergence criteria is derived. Furthermore, integral representation of this function has been established. Moreover, quadratic transformation,…
Range functions are a fundamental tool for certified computations in geometric modeling, computer graphics, and robotics, but traditional range functions have only quadratic convergence order ($m=2$). For ``superior'' convergence order…
This paper studies the approximation of generalized ridge functions, namely of functions which are constant along some submanifolds of $\mathbb{R}^N$. We introduce the notion of linear-sleeve functions, whose function values only depend on…
Recently, many researchers devoted their attention to study the extensions of the gamma and beta functions. In the present work, we focus on investigating some approximations for a class of Gauss hypergeometric functions by exploiting…