Hypergeometric symbolic calculus. I: Systems of two symbolic hypergeometric equations
type: Item
instance of: scholarly article
title: Hypergeometric symbolic calculus. I: Systems of two symbolic hypergeometric equations
zbMATH Open document ID: 1015.35023
DOI: 10.1016/S0007-4497(02)01143-0
author: Amédée Debiard
author: Bernard Gaveau
published in: Bulletin des Sciences Mathématiques
publication date: 2003-03-23T00:00:00Z
review text: The authors obtain the bases of solutions for all the 14 hypergeometric systems of Appel-Kampe de Feriet and Horn as well as integral representations for otherwise known solutions. They show that, in general, the space of solutions of a system consists of one analytic function in a neighborhood of the origin, and the other solutions are for most of the systems essentially a monomial \(x^\alpha y^\beta\) factor multiplied by an analytic function in a neighborhood of the origin. For certain systems there are special solutions which are convergent series in a cone \(|y / x |< \varepsilon\).
reviewed by: Vladimir L. Makarov
Mathematics Subject Classification ID: 35C05
Mathematics Subject Classification ID: 33C65
zbMATH DE Number: 1886879
zbMATH Keywords: bases of solutions
zbMATH Keywords: hypergeometric systems of Appel-Kampe de Feriet and Horn
zbMATH Keywords: integral representation
zbMATH Keywords: analytic function
MaRDI profile type: Publication
cites work: Q4753429
cites work: The analytic theory of systems of partial differential equations
cites work: Hypergeometric functions of two variables
cites work: Q5820721
cites work: Hypergeometrische Funktionen zweier Veränderlichen
cites work: Q4157418
cites work: Q5508372
full work available at URL: s0007-4497(02)01143-0
OpenAlex ID: W2091718501
Recommended article: Hypergeometric symbolic calculus. II: Systems of confluent equations
Recommended article: On hypergeometric systems of differential equations
Recommended article: General hypergeometric systems of equations and series of hypergeometric type
Recommended article: The structure of solutions of a hypergeometric equation system
Recommended article: On a fundamental system of solutions of a certain hypergeometric equation
Recommended article: On a multidimensional system of hypergeometric differential equations
Recommended article: Q3803293
Recommended article: Q3810025
Recommended article: Q5495393
Recommended article: Hypergeometric systems of Gelfand-type equations and series in orthogonal polynomials
description: scientific article; zbMATH DE number 1886879