Orthogonal polynomials and special functions [electronic resource] : computation and applications / F. Marcellán, W. van Assche (eds.)
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, bu...
Saved in:
| Online Access: |
Full Text (via Springer) |
|---|---|
| Other Authors: | , |
| Format: | Electronic eBook |
| Language: | English |
| Published: |
Berlin :
Springer,
©2006.
|
| Series: | Lecture notes in mathematics (Springer-Verlag) ;
1883. |
| Subjects: |
| Summary: | 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. |
|---|---|
| Physical Description: | 1 online resource (xiv, 418 pages) : illustrations, portrait. |
| Bibliography: | Includes bibliographical references and index. |
| ISBN: | 9783540367161 3540367160 3540310622 9783540310624 |
| ISSN: | 0075-8434 ; |
| Source of Description, Etc. Note: | Source of description: Print version record. |