Matrices de Stokes et groupe de Galois des équations hypergéometriques confluentes generalisées. (Stokes matrices and Galois groups of generalized confluent hypergeometric equations)
type: Item
instance of: scholarly article
title: Matrices de Stokes et groupe de Galois des équations hypergéometriques confluentes generalisées. (Stokes matrices and Galois groups of generalized confluent hypergeometric equations)
zbMATH Open document ID: 0705.34068
author: Anne Duval
author: Claude Mitschi
published in: Pacific Journal of Mathematics
publication date: 1989-01-01T00:00:00Z
review text: The authors consider the differential operator \[ D_{q,p}=(-1)^{q- p}z\prod^{p}_{j=1}(\vartheta +\mu_ j)-\prod^{q}_{j=1}(\vartheta +\nu_ j-1), \] where \(\vartheta\) stands for the Euler operator zd/dz; \(\mu_ 1,\mu_ 2,...,\nu_ q\) are given complex parameters while p and q are certain natural numbers such that \(\mu_ i-\mu_ j\) are not entire, \(p\geq 1\) and \(q\geq p+1\). Their main aim is to establish, in each one of certain appropriately designed consecutive sectors, a set of fundamental solutions to \(D_{q,p}u=0\) such that the asymptotic expansions of these solutions, valid near the point \(z=\infty\), are prescribed. In the first section of the paper they study the matrices (named: Stokes Matrices) which permit one to translate the system of solution valid in a sector to the solutions in the next sector over the intersections of these sectors. To this end they transform first the given equation through the Mellin transform and then use the classical inverse transform integral. The second section of the paper is devoted to the investigation of the group properties of the operators \(D_{3,1}\) and \(D_{3,2}\).
Mathematics Subject Classification ID: 34E05
zbMATH DE Number: 4156988
zbMATH Keywords: set of fundamental solutions
zbMATH Keywords: Stokes Matrices
zbMATH Keywords: Mellin transform
reviewed by: Mithat Idemen
MaRDI profile type: Publication
full work available at URL: pjm.1989.138.25
OpenAlex ID: W1982318194
DOI: 10.2140/PJM.1989.138.25
description: scientific article; zbMATH DE number 4156988