Lecture Notes in Mathematics

Orthogonal Polynomials and Special Functions

Computation and Applications

Editors: Marcellàn, Francisco, Van Assche, Walter (Eds.)

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About this book

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.

About the authors

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 (7 chapters)

Table of contents (7 chapters)
  • Orthogonal Polynomials, Quadrature, and Approximation: Computational Methods and Software (in Matlab)

    Pages 1-77

    Gautschi, Walter

  • Equilibrium Problems of Potential Theory in the Complex Plane

    Pages 79-117

    Finkelshtein, Andrei Martínez

  • Discrete Orthogonal Polynomials and Superlinear Convergence of Krylov Subspace Methods in Numerical Linear Algebra

    Pages 119-185

    Beckermann, Bernhard

  • Orthogonal Rational Functions on the Unit Circle: from the Scalar to the Matrix Case

    Pages 187-228

    Bultheel, Adhemar (et al.)

  • Orthogonal Polynomials and Separation of Variables

    Pages 229-254

    Kuznetsov, Vadim B.

Buy this book

eBook £47.99
price for United Kingdom (gross)
  • ISBN 978-3-540-36716-1
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover £59.99
price for United Kingdom (gross)
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Bibliographic Information

Bibliographic Information
Book Title
Orthogonal Polynomials and Special Functions
Book Subtitle
Computation and Applications
Editors
  • Francisco Marcellàn
  • Walter Van Assche
Series Title
Lecture Notes in Mathematics
Series Volume
1883
Copyright
2006
Publisher
Springer-Verlag Berlin Heidelberg
Copyright Holder
Springer-Verlag Berlin Heidelberg
eBook ISBN
978-3-540-36716-1
DOI
10.1007/b128597
Softcover ISBN
978-3-540-31062-4
Series ISSN
0075-8434
Edition Number
1
Number of Pages
XIV, 422
Topics