Orthogonal Polynomials and Special Functions Computation and Applica

Special functions and orthogonal polynomials in particular have been around for centuries. Can you imagine mathematics without trigonometric functions, the exponential function or polynomials? In the twentieth century the emphasis was on special functions

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Lecture Notes in Mathematics Editors: J.-M. Morel, Cachan F. Takens, Groningen B. Teissier, Paris

1883

F. Marcellán · W.Van Assche (Eds.)

Orthogonal Polynomials and Special Functions Computation and Applications

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Editors Francisco Marcellán Departamento de Matemáticas Universidad Carlos III de Madrid Avenida de la Universidad 30 28911 Leganés Spain e-mail: [email protected]

Walter Van Assche Department of Mathematics Katholieke Universiteit Leuven Celestijnenlaan 200B 3001 Leuven Belgium e-mail: [email protected]

Library of Congress Control Number: 2006923695 Mathematics Subject Classification (2000): 33C45, 33C50, 33E17, 33F05, 42C05, 41A55 65E05, 65F15, 65F25 ISSN print edition: 0075-8434 ISSN electronic edition: 1617-9692 ISBN-10 3-540-31062-2 Springer Berlin Heidelberg New York ISBN-13 978-3-540-31062-4 Springer Berlin Heidelberg New York DOI 10.1007/b128597

This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilm 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. Violations are liable for prosecution under the German Copyright Law. Springer is a part of Springer Science+Business Media springer.com c Springer-Verlag Berlin Heidelberg 2006  Printed in The Netherlands The use of general descriptive names, registered names, trademarks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. A EX package Typesetting: by the authors and SPI Publisher Services using a Springer LT Cover design: design & production GmbH, Heidelberg

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543210

Preface

These are the lecture notes of the fifth European summer school on Orthogonal Polynomials and Special Functions, which was held at the Universidad Carlos III de Madrid, Legan´es, Spain from July 8 to July 18, 2004. Previous summer schools were in Laredo, Spain (2000) [1], Inzell, Germany (2001) [2], Leuven, Belgium (2002) [3] and Coimbra, Portugal (2003) [4]. These summer schools are intended for young researchers preparing a doctorate or Ph.D. and postdocs working in the area of special functions. For this edition we were happy to have eight invited speakers who gave a series of lectures on a subject for which they are internationally known experts. Seven of these lectures are collected in this volume. The lecture of J. S. Geronimo on WKB and turning point theory for second order difference equations has been published els