Lectures On Orthogonal Polynomials And Special Functions
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Laredo Lectures on Orthogonal Polynomials and Special Functions
This new book presents research in orthogonal polynomials and special functions. Recent developments in the theory and accomplishments of the last decade are pointed out and directions for research in the future are identified. The topics covered include matrix orthogonal polynomials, spectral theory and special functions, Asymptotics for orthogonal polynomials via Riemann-Hilbert methods, Polynomial wavelets and Koornwinder polynomials.
Lectures on Orthogonal Polynomials and Special Functions
Author: Howard S. Cohl
language: en
Publisher: Cambridge University Press
Release Date: 2020-10-15
Contains graduate-level introductions by international experts to five areas of research in orthogonal polynomials and special functions.
Orthogonal Polynomials and Special Functions
Author: Francisco Marcellàn
language: en
Publisher: Springer Science & Business Media
Release Date: 2006-06-19
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 satisfying linear differential equations, but this has now been extended to difference equations, partial differential equations and non-linear differential equations. The present set of lecture notes containes seven chapters about the current state of orthogonal polynomials and special functions and gives a view on open problems and future directions. The topics are: computational methods and software for quadrature and approximation, equilibrium problems in logarithmic potential theory, discrete orthogonal polynomials and convergence of Krylov subspace methods in numerical linear algebra, orthogonal rational functions and matrix orthogonal rational functions, orthogonal polynomials in several variables (Jack polynomials) and separation of variables, a classification of finite families of orthogonal polynomials in Askey’s scheme using Leonard pairs, and non-linear special functions associated with the Painlevé equations.