Orthogonal Polynomials and Special Functions: Leuven 2002

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. Computer Algebra Algorithms for Orthogonal Polynomials and Special Functions....Pages 1-24 3 nj -Coefficients and Orthogonal Polynomials of Hypergeometric Type....Pages 25-92 Dunkl Operators: Theory and Applications....Pages 93-135 Enumeration and Special Functions....Pages 137-166 Riemann-Hilbert Analysis for Orthogonal Polynomials....Pages 167-210 Exponential Asymptotics....Pages 211-244