Chapter 18 Orthogonal Polynomials
T. H. Koornwinder
Affiliation: University of Amsterdam,
Korteweg–de Vries Institute,
Amsterdam, The Netherlands.
R. Wong
Affiliation: City University of Hong Kong,
Liu Bie Ju Centre for Mathematical Sciences,
Kowloon,
Hong Kong.
R. Koekoek
Affiliation: Delft University of Technology,
Delft Institute of Applied Mathematics,
Delft, The Netherlands.
R. F. Swarttouw
Affiliation: Delft University of Technology,
Delft Institute of Applied Mathematics,
Delft, The Netherlands.
W. P. Reinhardt
Affiliation: University of Washington,
Department of Chemistry,
Seattle, Washington, USA.
ⓘ
- Notes:
- The main references for writing this chapter are Andrews et al. (1999), Askey and Wilson (1985), Chihara (1978), Koekoek et al. (2010), and Szegő (1975).
- Referenced by:
- §14.7(i), §16.7, §3.11(ii), DLMF Update; Version 1.2.0, Profile René F. Swarttouw, Profile Roelof Koekoek, Profile Roderick S. C. Wong, Profile Roderick S. C. Wong, Profile Tom H. Koornwinder, Profile Wolter Groenevelt, § ‣ Chapter Authors, § ‣ Chapter Authors, § ‣ Chapter Authors, § ‣ Chapter Authors, § ‣ Associate Editors, § ‣ Associate Editors, § ‣ Contributing Developers, Erratum (V1.0.20) for Chapter 18 Orthogonal Polynomials, Erratum (V1.1.6) for Chapters 10 Bessel Functions, 18 Orthogonal Polynomials, 34 3j, 6j, 9j Symbols, Erratum (V1.1.6) for Chapters 1 Algebraic and Analytic Methods, 10 Bessel Functions, 14 Legendre and Related Functions, 18 Orthogonal Polynomials, 29 Lamé Functions, Erratum (V1.2.0) for Chapter 18 Additions, Version 1.2.0 (March 27, 2024), Version 1.2.0 (March 27, 2024), Organization and Objective, § ‣ Software Cross Index
- Permalink:
- http://dlmf.nist.gov/18
- Notation
- General Orthogonal Polynomials
-
Classical Orthogonal Polynomials
- 18.3 Definitions
- 18.4 Graphics
- 18.5 Explicit Representations
- 18.6 Symmetry, Special Values, and Limits to Monomials
- 18.7 Interrelations and Limit Relations
- 18.8 Differential Equations
- 18.9 Recurrence Relations and Derivatives
- 18.10 Integral Representations
- 18.11 Relations to Other Functions
- 18.12 Generating Functions
- 18.13 Continued Fractions
- 18.14 Inequalities
- 18.15 Asymptotic Approximations
- 18.16 Zeros
- 18.17 Integrals
- 18.18 Sums
-
Askey Scheme
- 18.19 Hahn Class: Definitions
- 18.20 Hahn Class: Explicit Representations
- 18.21 Hahn Class: Interrelations
- 18.22 Hahn Class: Recurrence Relations and Differences
- 18.23 Hahn Class: Generating Functions
- 18.24 Hahn Class: Asymptotic Approximations
- 18.25 Wilson Class: Definitions
- 18.26 Wilson Class: Continued
-
Other Orthogonal Polynomials
- 18.27 -Hahn Class
- 18.28 Askey–Wilson Class
- 18.29 Asymptotic Approximations for -Hahn and Askey–Wilson Classes
- 18.30 Associated OP’s
- 18.31 Bernstein–Szegő Polynomials
- 18.32 OP’s with Respect to Freud Weights
- 18.33 Polynomials Orthogonal on the Unit Circle
- 18.34 Bessel Polynomials
- 18.35 Pollaczek Polynomials
- 18.36 Miscellaneous Polynomials
- 18.37 Classical OP’s in Two or More Variables
- Applications
- Computation