On a hypergeometric function of four variables with a new aspect of \(SL\)- symmetry
type: Item
instance of: scholarly article
title: On a hypergeometric function of four variables with a new aspect of \(SL\)- symmetry
zbMATH Open document ID: 0781.33007
DOI: 10.1007/BF01759644
published in: Annali di Matematica Pura ed Applicata. Serie Quarta
publication date: 1993-01-16T00:00:00Z
review text: The hypergeometric function under consideration is the author's \(K_{16}\). (It is also denoted by \(H_ C^{(4)}\).) A system of four partial differential equations for this function is obtained, and their singular manifolds are given. The system has 21 essentially different singular points in \(\mathbb{C}^ 4\). Some properties of \(K_{16}\) are given: an Euler transformation and a Pochhammer integral representation. Next, it is shown that the system of PDE's has further solutions in terms of \(K_{16}\) and two more quadruple hypergeometric functions. After these preparations the author can finally present, for each of the 21 singularities, a list of six linearly independent integrals of the system of PDE's. The expressions are too long to reproduce here.
Mathematics Subject Classification ID: 33C70
zbMATH DE Number: 95003
zbMATH Keywords: bisingularities for PDE's
zbMATH Keywords: hypergeometric PDE's
author: H. Exton
reviewed by: Per W. Karlsson
MaRDI profile type: Publication
cites work: Hypergeometric functions of two variables
cites work: Q4103811
cites work: Multiple Hypergeometric Functions and Simple Lie Groups ${\bf {\text{SL}}}$ and ${\bf {\text{Sp}}}$
cites work: Q4093754
cites work: Integration of the Partial Differential Equations for the Hypergeometric Functions F1 and FD of Two and More Variables
cites work: On the integration of the differential equations of five-parametric double-hypergeometric functions of second order
description: scientific article; zbMATH DE number 95003