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 $q$-Analogues) Hypergeometric Orthogonal Polynomials and Their $q$-Analogues. … ►

18 Orthogonal Polynomials

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2: 18.37 Classical OP’s in Two or More Variables

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Orthogonality

… ►The following three conditions, taken together, determine $R_{m,n}^{(\alpha )}\left(z\right)$ uniquely: … ►

§18.37(ii) OP’s on the Triangle

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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. …

3: 18 Orthogonal Polynomials

Chapter 18 Orthogonal Polynomials

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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. … ►

18 Orthogonal Polynomials

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6: 32.15 Orthogonal Polynomials

§32.15 Orthogonal Polynomials

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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. …

9: 18.21 Hahn Class: Interrelations

§18.21 Hahn Class: Interrelations

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§18.21(i) Dualities

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§18.21(ii) Limit Relations and Special Cases

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Hahn $\to$ Jacobi

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Meixner $\to$ Laguerre

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10: 18.3 Definitions

§18.3 Definitions

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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. …