Results of Orthogonal Polynomials

Notation

18.1 Notation

General Orthogonal Polynomials

18.2 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 ${\displaystyle{\displaystyle q}}$ -Hahn Class
18.28 Askey–Wilson Class
18.29 Asymptotic Approximations for ${\displaystyle{\displaystyle q}}$ -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

18.38 Mathematical Applications
18.39 Physical Applications

Computation

18.40 Methods of Computation
18.41 Tables
18.42 Software