Special functions 2000: current perspective and future directions

The Advanced Study Institute brought together researchers in the main areas of special functions and applications to present recent developments in the theory, review the accomplishments of past decades, and chart directions for future research. Some of the topics covered are orthogonal polynomials and special functions in one and several variables, asymptotic, continued fractions, applications to number theory, combinatorics and mathematical physics, integrable systems, harmonic analysis and quantum groups, Painlevé classification.

Bailey's transform, lemma, chains and tree -- Riemann-Hilbert problems for multiple orthogonal polynomials -- Flowers which we cannot yet see growing in Ramanujan's garden of hypergeometric series, elliptic functions and q's -- Orthogonal rational functions and continued fractions -- Orthogonal polynomials and reflection groups -- The bispectral problem: an overview -- The Bochner-Krall problem: some new perspectives -- Lectures on q-orthogonal polynomials -- The Askey-Wilson function transform scheme -- Arithmetic of the partition function -- The associated classical orthogonal polynomials -- Special functions defined by analytic difference equations -- The factorization method, self-similar potentials and quantum algebras -- Generalized eigenvalue problem and a new family of rational functions biorthogonal on elliptic grids -- Orthogonal polynomials and combinatorics -- Basic exponential functions on a q-quadratic grid -- Projection operator method for quantum groups -- Uniform asymptotic expansions -- Exponential asymptotics.