orthogonality

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1: René F. Swarttouw
Swarttouw is mainly a teacher of mathematics and has published a few papers on special functions and orthogonal polynomials. He is coauthor of the book Hypergeometric Orthogonal Polynomials and Their $q$-AnaloguesHypergeometric Orthogonal Polynomials and Their $q$-Analogues. …
• 2: 18.37 Classical OP’s in Two or More Variables
Orthogonality
The following three conditions, taken together, determine $R^{(\alpha)}_{m,n}\left(z\right)$ uniquely: …
Orthogonality
Orthogonal polynomials associated with root systems are certain systems of trigonometric polynomials in several variables, symmetric under a certain finite group (Weyl group), and orthogonal on a torus. …
4: 16.7 Relations to Other Functions
§16.7 Relations to Other Functions
For orthogonal polynomials see Chapter 18. …
5: Roelof Koekoek
Koekoek is mainly a teacher of mathematics and has published a few papers on orthogonal polynomials. He is also author of the book Hypergeometric Orthogonal Polynomials and Their $q$-Analogues (with P. …
7: Wolter Groenevelt
Groenevelt’s research interests is in special functions and orthogonal polynomials and their relations with representation theory and interacting particle systems. As of September 20, 2022, Groenevelt performed a complete analysis and acted as main consultant for the update of the source citation and proof metadata for every formula in Chapter 18 Orthogonal Polynomials. …
8: 12.16 Mathematical Applications
For examples see §§13.20(iii), 13.20(iv), 14.15(v), and 14.26. Sleeman (1968b) considers certain orthogonality properties of the PCFs and corresponding eigenvalues. …
10: 18.3 Definitions
§18.3 Definitions
• 3.

As given by a Rodrigues formula (18.5.5).

• Table 18.3.1 provides the traditional definitions of Jacobi, Laguerre, and Hermite polynomials via orthogonality and standardization (§§18.2(i) and 18.2(iii)). … For another version of the discrete orthogonality property of the polynomials $T_{n}\left(x\right)$ see (3.11.9). … However, in general they are not orthogonal with respect to a positive measure, but a finite system has such an orthogonality. …