Orthogonal Polynomials and Special Functions: Computation and Applications

by Francisco Marcellàn (Editor), Walter Van Assche (Editor)

Overview

Special functions and orthogonal polynomials in particular have been around for centuries. Can you imagine mathematics without trigonometric functions, the exponential function or polynomials? The present set of lecture notes contains seven chapters about the current state of orthogonal polynomials and special functions and gives a view on open problems and future directions.

Product Details

ISBN-13:	9783540310624
Publisher:	Springer Berlin Heidelberg
Publication date:	07/26/2006
Series:	Lecture Notes in Mathematics , #1883
Edition description:	2006
Pages:	422
Product dimensions:	0.00(w) x 0.00(h) x 0.36(d)

About the Author

Francisco Marcellán is full professor of applied mathematics at the Universidad Carlos III de Madrid in Leganés (Spain) where he served as vice rector of research. In the past he has been teaching at the universities of Zaragoza, Santiago de Compostela and the Polytécnica de Madrid and was recently a visiting professor at the Georgia Institute of Technology. He was program director of the SIAM activity group on Orthogonal Polynomials and Special Functions from 1999 to 2005. Presently he is the director of the Spanish National Agency for Quality Assurance and Accreditation (ANECA). He has several publications in mathematical analysis (most particularly special functions and approximation) and linear algebra.

Walter Van Assche is full professor of mathematics at the Katholieke Universiteit Leuven in Belgium and was a research director of the Belgian National Fund for Scientific Research. He was vice chair of the SIAM activity group on Orthogonal Polynomials and Special Functions from 1999 to 2005 and is on the editorial board of the Journal of Approximation Theory and the Journal of Difference Equations and Applications. He is the author of Asymptotics for Orthogonal Polynomials (Lecture Notes in Mathematics 1265) and wrote two chapters in M.E.H. Ismail’s book Classical and Quantum Orthogonal Polynomials in one Variable.

Table of Contents

Orthogonal Polynomials, Quadrature, and Approximation: Computational Methods and Software (in Matlab).- Equilibrium Problems of Potential Theory in the Complex Plane.- Discrete Orthogonal Polynomials and Superlinear Convergence of Krylov Subspace Methods in Numerical Linear Algebra.- Orthogonal Rational Functions on the Unit Circle: from the Scalar to the Matrix Case.- Orthogonal Polynomials and Separation of Variables.- An Algebraic Approach to the Askey Scheme of Orthogonal Polynomials.- Painlevé Equations — Nonlinear Special Functions.