orthogonality
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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 Hypergeometric Orthogonal Polynomials and Their
-Analogues) Hypergeometric Orthogonal Polynomials and Their -Analogues.
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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 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: 18.36 Miscellaneous Polynomials
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►Sobolev OP’s are orthogonal with respect to an inner product involving derivatives.
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§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: 18 Orthogonal Polynomials
Chapter 18 Orthogonal Polynomials
…5: 16.7 Relations to Other Functions
6: 18.40 Methods of Computation
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►Orthogonal polynomials can be computed from their explicit polynomial form by Horner’s scheme (§1.11(i)).
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►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.
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7: 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 -Analogues (with P.
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8: 18.38 Mathematical Applications
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Quadrature
… ►Integrable Systems
… ►Riemann–Hilbert Problems
… ►Radon Transform
… ►Group Representations
…9: Wolter Groenevelt
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►Groenevelt has research interests in special functions, (matrix valued) orthogonal polynomials, moment problems, generalized Fourier transforms in relations with mathematical objects such as Lie algebras, quantum groups and affine Hecke algebras.
►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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