Orthogonal Polynomials and Special Functions Leuven 2002
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Erik Koelink Walter Van Assche (Eds.)
Orthogonal Polynomials and Special Functions Leuven 2002
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Editors Erik Koelink Afd. Toegepaste Wiskundige Analyse EWI-TWA, Technische Universiteit Delft Postbus 5031 2600 GA Delft, Netherlands e-mail: [email protected] http://fa.its.tudelft.nl/˜koelink Walter Van Assche Departement Wiskunde Katholieke Universiteit Leuven Celestijnenlaan 200B 3001 Leuven, Belgium e-mail: [email protected] http://www.wis.kuleuven.ac.be/analyse/walter
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Mathematics Subject Classification (2000): 33-01, 33F10, 68W30, 33C80, 22E47, 33C52, 05A15, 34E05, 34M40, 42C05, 30E25, 41A60 ISSN 0075-8434 ISBN 3-540-40375-2 Springer-Verlag Berlin Heidelberg New York This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specif ically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microf ilm or in any other way, and storage in data banks. Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9, 1965, in its current version, and permission for use must always be obtained from Springer-Verlag. Violations are liable for prosecution under the German Copyright Law. Springer-Verlag Berlin Heidelberg New York a member of BertelsmannSpringer Science + Business Media GmbH http://www.springer.de c Springer-Verlag Berlin Heidelberg 2003 Printed in Germany The use of general descriptive names, registered names, trademarks, etc. in this publication does not imply, even in the absence of a specif ic statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. Typesetting: Camera-ready TEX output by the author SPIN: 10933602
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Preface
Orthogonal Polynomials and Special Functions (OPSF) is a very old branch of mathematics having a very rich history. Many famous mathematicians have contributed to the subject: Euler’s work on the gamma function, Gauss’s and Riemann’s work on the hypergeometric functions and the hypergeometric differential equation, Abel’s and Jacobi’s work on elliptic functions, and so on. Usually the special functions have been introduced to solve a specific problem, and many of them occurred in solving the differential equations describing a physical problem, e.g., the astronomer Bessel introduced the functions named after him in his work on Kepler’s problem of three bodies moving under mutual gravitation. So the subject OPSF is very classical and there have been very interesting developments through the centuries, and there have been numerous applic
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