# 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. …
##### 3: 18.36 Miscellaneous Polynomials
Sobolev OP’s are orthogonal with respect to an inner product involving derivatives. …
###### §18.36(iii) Multiple OP’s
These are polynomials in one variable that are orthogonal with respect to a number of different measures. …
###### §18.36(iv) Orthogonal Matrix Polynomials
These are matrix-valued polynomials that are orthogonal with respect to a square matrix of measures on the real line. …
##### 4: 16.7 Relations to Other Functions
###### §16.7 Relations to Other Functions
For orthogonal polynomials see Chapter 18. …
##### 5: 18.40 Methods of Computation
Orthogonal polynomials can be computed from their explicit polynomial form by Horner’s scheme (§1.11(i)). … However, for applications in which the OP’s appear only as terms in series expansions (compare §18.18(i)) the need to compute them can be avoided altogether by use instead of Clenshaw’s algorithm (§3.11(ii)) and its straightforward generalization to OP’s other than Chebyshev. …
##### 6: 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: 18.38 Mathematical Applications
The corresponding eigenfunctions are … For physical applications of $q$-Laguerre polynomials see §17.17. …