The General Theory of Differential Equations
In this chapter we recall some basic facts about systems of linear partial differential equations in the single unknown on open subsets of ℂn. Since the ring of linear partial differential operators is not a principal ideal domain when n ≧ 2, the situatio
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Masaaki Yoshida
Fuchsian differential equations With special emphasis on the Gauss-Schwarz theory
Masaaki Yoshida
Fuchsian Differential Equations
Asp3ds of Mathematics As~derMathematik
Editor: Klas Diederich
Vol. EJ:
G. Hector/U. Hirsch, lntroduction to the Geometry of Foliatians, Part A
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M. Knebusch/M. Kolster, Wittrings
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G. Hector/U. Hirsch, lntraduction ta the Geometry of Foliations, Part B
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M. Laska, Elliptic Curves over Number Fields with Prescribed Reduction Type
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G. Faltings/G. Wüstholzet al., Rational Points (A Publication of the Max-Pianck-lnstitut für Mathematik, Bonn)
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W. von Wahl, The Equations of Navier-Stokes and Abstract Parabolic Equations
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A. Haward, P.-M. Wong (Eds.), Contributians to Several Camplex Variables
Vol. E10: A. J. Tromba, Seminar on New Results in Nonlinear Partial Differential Equations (A Publication of the Max-Pianck-lnstitut für Mathematik, Bonn)
Vol. E11: M. Yoshida, Fuchsian Differential Equations (A Pub I ication of the Max-Pianck-1 nstitut für Mathematik, Bonn)
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H. Kraft, Geometrische Methoden in der Invariantentheorie
Masaaki Yoshida
Fuchsian Differential Equations With Special Emphasis on the Gauss-Schwarz Theory
A Publication of the Max-Pianck-lnstitut für Mathematik, Bann Adviser: Friedrich Hirzebruch
Springer Fachmedien Wiesbaden GmbH
Professor Masaaki Yoshida Kyushu University , Fukuoka, Japan
AMS Subject Classification : 35 R 25, 35R 30, 45A05 , 45 L05, 65F 20
1987 All rights reserved © Springer FachmedienWiesbaden 1987 Originally published by Friedr.Vieweg & Sohn VerlagsgesellschaftmbH, Braunschweig in 1987.
No part of th is publication may be reproduced , stored in a retrieval system or transmitted in any form or by any means, electronic, mechan ical , photocopying, recording or otherwise, w ithout prior permission of the copyright holder .
Produced by W. Langelüddecke , Braunschweig
ISSN
0179-2156
ISBN 978-3-528-08971-9 ISBN 978-3-663-14115-0 (eBook) DOI 10.1007/978-3-663-14115-0
Contents
Introduetion Notations Part
I
Chapter 1 § 1.1 1.2 § 1.3 1.4 1.5 1.6
Hypergeometrie Differential Equations ........... 1 Hypergeometrie Series ........................... 1 Hypergeometrie Equations ........................ 2 Contiguity Relations ............................ 3 Euler's Integral Representation ................. 5 Rarnes' Integral Representation ................ 11 Lonfluent Hypergeometrie Equations ............. 12
Chapter 2 § 2.1 § 2. 2 2. 3
General Theory of Differential Equations I .... 14 How to Write Differential Equations ............ 14 Cauehy's Fundamental Theorem ................... 15 Monodromy Representations of Differential Equations ....................................... 16 Regular Singularities .......................... 18 The Frobenius Method ........................... 20 Fuehsian Equations ..........
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