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July 2015 On certain conformally invariant systems of differential equations II: Further study of type A systems
Anthony C. Kable
Tsukuba J. Math. 39(1): 39-81 (July 2015). DOI: 10.21099/tkbjm/1438951817

Abstract

Previously, several families of systems of differential equations that generalize the Heisenberg Laplacian equations were introduced. The study of one of these families is continued here. It is shown that the systems in this family are free of integrability conditions provided that a parameter appearing in the system avoids a certain set of bad values, which is explicitly determined. Properties of polynomial solutions to the systems are investigated and special polynomial solutions involving terminating Lauricella hypergeometric series are given in some cases.

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Anthony C. Kable. "On certain conformally invariant systems of differential equations II: Further study of type A systems." Tsukuba J. Math. 39 (1) 39 - 81, July 2015. https://doi.org/10.21099/tkbjm/1438951817

Information

Published: July 2015
First available in Project Euclid: 7 August 2015

zbMATH: 1342.35423
MathSciNet: MR3383878
Digital Object Identifier: 10.21099/tkbjm/1438951817

Subjects:
Primary: 35R03
Secondary: 22E25 , 33C65 , 35C11

Keywords: Heisenberg Laplacian , Lauricella hypergeometric polynomial , module of polynomial solutions , systems of differential equations on nilpotent groups

Rights: Copyright © 2015 University of Tsukuba, Institute of Mathematics

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Vol.39 • No. 1 • July 2015
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