Rogers–Szegő polynomials
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31: 18.36 Miscellaneous Polynomials
§18.36 Miscellaneous Polynomials
►§18.36(i) Jacobi-Type Polynomials
… ►§18.36(ii) Sobolev Orthogonal Polynomials
… ►§18.36(iv) Orthogonal Matrix Polynomials
… ►§18.36(vi) Exceptional Orthogonal Polynomials
…32: 18.37 Classical OP’s in Two or More Variables
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§18.37(i) Disk Polynomials
►Definition in Terms of Jacobi Polynomials
… ►Definition in Terms of Jacobi Polynomials
… ►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. …For general they occur as Macdonald polynomials for root system , as Macdonald polynomials for general root systems, and as Macdonald–Koornwinder polynomials; see Macdonald (1995, Chapter VI), Macdonald (2000, 2003), Koornwinder (1992).33: 24.4 Basic Properties
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§24.4(i) Difference Equations
… ►§24.4(ii) Symmetry
… ►Next, … ►§24.4(vi) Special Values
… ►§24.4(vii) Derivatives
…34: 18.10 Integral Representations
35: 18.5 Explicit Representations
36: 18.35 Pollaczek Polynomials
§18.35 Pollaczek Polynomials
… ►There are 3 types of Pollaczek polynomials: … ►For the monic polynomials … ► … ► …37: 24.16 Generalizations
§24.16 Generalizations
… ►Polynomials and Numbers of Integer Order
… ►Nörlund Polynomials
… ►§24.16(ii) Character Analogs
… ►§24.16(iii) Other Generalizations
…38: 18.18 Sums
39: 29.20 Methods of Computation
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►These matrices are the same as those provided in §29.15(i) for the computation of Lamé polynomials with the difference that has to be chosen sufficiently large.
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►A fourth method is by asymptotic approximations by zeros of orthogonal polynomials of increasing degree.
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