Orthogonal Polynomials and Special Functions: Leuven 2002: 1817 (Lecture Notes in Mathematics, 1817) - Softcover

Softcover

ISBN 10: 3540403752 ISBN 13: 9783540403753

Publisher: Springer, 2003

Synopsis

OrthogonalPolynomialsandSpecialFunctions(OPSF)is a veryoldbranchof 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 onthe hypergeometricfunctions andthe hypergeometric di?erentialequation,Abel's andJacobi'sworkonelliptic functions,andsoon. Usuallythespecialfunctionshavebeenintroducedto solveaspeci?cproblem, and many of them occurred in solving the di?erential equations describing a physical problem, e.g., the astronomerBessel introduced the functions named afterhiminhisworkonKepler'sproblemofthreebodiesmovingundermutual gravitation. So the subject OPSF is very classical and there have been very interesting developments through the centuries, and there have been numerous appli- tions to various branches of mathematics, e.g. combinatorics, representation theory,numbertheory,andapplicationstophysicsandastronomy,suchasthe afore-mentioned classical physical problems, but also integrable systems, - tics,quantumchemistry,etcetera.SoOPSFiswell-established,andverymuch driven by applications. The advent of the computer, ?rst thought to be fatal to the subject, turned out to be a stimulus, ? rst of all because it allowedmore detailed computations requiring special numerical algorithms, but mainly - cause it led to automatic summation routines, notably the WZ-method (see Koepf's contribution). So OPSF is a very lively branch of mathematics. Since more advanced courses on OPSF seldom appear in the curriculum, we felt the need for such courses for young researchers (graduate students and post-docs). A series of European summer schools was started with one in Laredo, Spain (2000) and one in Inzell, Germany (2001). This book contains the notes for the lectures of the summer school in Belgium in 2002, which took place from August 12-16, 2002, at the Katholieke Universiteit Leuven, Belgium.In2003asummerschoolinOPSFwillbeheldinCoimbra,Portugal.

About this title

Product Description

The set of lectures from the Summer School held in Leuven in 2002 provide an up-to-date account of recent developments in orthogonal polynomials and special functions, in particular for algorithms for computer algebra packages, 3nj-symbols in representation theory of Lie groups, enumeration, multivariable special functions and Dunkl operators, asymptotics via the Riemann-Hilbert method, exponential asymptotics and the Stokes phenomenon. The volume aims at graduate students and post-docs working in the field of orthogonal polynomials and special functions, and in related fields interacting with orthogonal polynomials, such as combinatorics, computer algebra, asymptotics, representation theory, harmonic analysis, differential equations, physics. The lectures are self-contained requiring only a basic knowledge of analysis and algebra, and each includes many exercises.

Edition details

• Publisher: Springer
• Publication date: 2003
• Language: English
• ISBN 10: 3540403752
• ISBN 13: 9783540403753
• Binding: Paperback
• Number of pages: 260
• Editor: Koelink Erik, Van Assche Walter