Bustoz J., Ismail M.E.H., Suslov S.K. (Eds.) Special Functions 2000: Current Perspective and Future Directions

Springer Science+Business Media, Dordrecht, 2001. – 521 p. – ISBN: 0792371208The 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