Chapter 18 Orthogonal Polynomials
- Notes:
- The main references for writing this chapter are Andrews et al. (1999), Askey and Wilson (1985), Chihara (1978), Koekoek et al. (2010), and Szegö (1975).
- Referenced by:
- §14.7(i), §16.7, §3.11(ii), René F. Swarttouw, Roelof Koekoek, Roderick S. C. Wong, Tom H. Koornwinder, Organization and Objective, § ‣ § Software Cross Index
- Permalink:
- http://dlmf.nist.gov/18
University of Amsterdam,
Korteweg–de Vries Institute,
Amsterdam, The Netherlands.
City University of Hong Kong,
Liu Bie Ju Centre for Mathematical Sciences,
Kowloon,
Hong Kong.
Delft University of Technology,
Delft Institute of Applied Mathematics,
Delft, The Netherlands.
Vrije Universiteit Amsterdam,
Department of Mathematics,
Amsterdam, The Netherlands.
- 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–Szegö 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
- 18.27
- Applications
- Computation