orthogonality

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11: 29 Lamé Functions

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12: 18.1 Notation

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Classical OP’s

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Hahn Class OP’s

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Wilson Class OP’s

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Disk: $R_{m,n}^{(\alpha )}\left(z\right)$.

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Triangle: $P_{m,n}^{\alpha ,\beta ,\gamma }(x,y)$.

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13: 18.38 Mathematical Applications

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Quadrature

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Riemann–Hilbert Problems

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Radon Transform

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Group Representations

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Dunkl Type Operators and Nonsymmetric Orthogonal Polynomials

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14: 10 Bessel Functions

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15: Howard S. Cohl

… ►Cohl has published papers in orthogonal polynomials and special functions, and is particularly interested in fundamental solutions of linear partial differential equations on Riemannian manifolds, associated Legendre functions, generalized and basic hypergeometric functions, eigenfunction expansions of fundamental solutions in separable coordinate systems for linear partial differential equations, orthogonal polynomial generating function and generalized expansions, and $q$-series. …

16: Tom H. Koornwinder

… ►Koornwinder has been active as an officer in the SIAM Activity Group on Special Functions and Orthogonal Polynomials. … ►

18 Orthogonal Polynomials

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17: Richard A. Askey

… ►Over his career his primary research areas were in Special Functions and Orthogonal Polynomials, but also included other topics from Classical Analysis and related areas. …One of his most influential papers Some basic hypergeometric orthogonal polynomials that generalize Jacobi polynomials (with J. …Published in 1985 in the Memoirs of the American Mathematical Society, it also introduced the directed graph of hypergeometric orthogonal polynomials commonly known as the Askey scheme. … ►Additional books for which Askey served as author or editor include Orthogonal Polynomials and Special Functions, published by SIAM in 1975, Theory and application of special functions, published by Academic Press in 1975, Special Functions: Group Theoretical Aspects and Applications (with T. … ►Askey was presented a Lifetime Achievement Award in Recognition and Appreciation for his Outstanding Work and Leadership in the Field of Special Functions at the International Symposium on Orthogonal Polynomials, Special Functions and Applications in Hagenberg, Austria on July 24, 2019. …

18: 18.36 Miscellaneous Polynomials

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§18.36(ii) Sobolev Orthogonal Polynomials

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§18.36(iii) Multiple Orthogonal Polynomials

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§18.36(iv) Orthogonal Matrix Polynomials

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§18.36(vi) Exceptional Orthogonal Polynomials

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19: 18.19 Hahn Class: Definitions

§18.19 Hahn Class: Definitions

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Hahn, Krawtchouk, Meixner, and Charlier

… ►These polynomials are orthogonal on $(-\mathrm{\infty },\mathrm{\infty })$, and with $\mathrm{\Re }a>0$, $\mathrm{\Re }b>0$ are defined as follows. … ►These polynomials are orthogonal on $(-\mathrm{\infty },\mathrm{\infty })$, and are defined as follows. …A special case of (18.19.8) is $w^{(1/2)}(x;\pi /2)=\frac{\pi }{\cosh \left(\pi x\right)}$.

20: 18.41 Tables

… ►For $P_n\left(x\right)$ ($={𝖯}_n\left(x\right)$) see §14.33. …