# orthogonality

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## 1—10 of 137 matching pages

##### 1: René F. Swarttouw

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

… ►###### 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

…##### 4: 16.7 Relations to Other Functions

##### 5: Roelof Koekoek

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►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.
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##### 6: 32.15 Orthogonal Polynomials

###### §32.15 Orthogonal Polynomials

… ►##### 7: Wolter Groenevelt

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►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.
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##### 8: 12.16 Mathematical Applications

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►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.
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##### 9: 18.21 Hahn Class: Interrelations

###### §18.21 Hahn Class: Interrelations

►###### §18.21(i) Dualities

… ►###### §18.21(ii) Limit Relations and Special Cases

… ►###### Hahn $\to $ Jacobi

… ►###### Meixner $\to $ Laguerre

…##### 10: 18.3 Definitions

###### §18.3 Definitions

… ►As given by a *Rodrigues formula* (18.5.5).

*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. …