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In mathematics, a Szegő polynomial is one of a family of orthogonal polynomials for the Hermitian inner product f | g = ∫ − π π f ( e i θ ) g ( e i θ ) ¯ d μ {\displaystyle \langle f|g\rangle =\int _{-\pi }^{\pi }f(e^{i\theta }){\overline {g(e^{i\theta })}}\,d\mu }
The Macdonald polynomials are orthogonal polynomials in several variables, depending on the choice of an affine root system. They include many other families of multivariable orthogonal polynomials as special cases, including the Jack polynomials, the Hall–Littlewood polynomials, the Heckman–Opdam polynomials, and the Koornwinder polynomials.
Gábor Szegő (Hungarian: [ˈɡaːbor ˈsɛɡøː]) (January 20, 1895 – August 7, 1985) was a Hungarian-American mathematician.He was one of the foremost mathematical analysts of his generation and made fundamental contributions to the theory of orthogonal polynomials and Toeplitz matrices building on the work of his contemporary Otto Toeplitz.
In mathematics, orthogonal polynomials on the unit circle are families of polynomials that are orthogonal with respect to integration over the unit circle in the complex plane, for some probability measure on the unit circle. They were introduced by Szegő (1920, 1921, 1939).
In mathematics, the Rogers–Szegő polynomials are a family of polynomials orthogonal on the unit circle introduced by Szegő , who was inspired by the continuous q-Hermite polynomials studied by Leonard James Rogers. They are given by
In mathematics, Jacobi polynomials (occasionally called hypergeometric polynomials) (,) are a class of classical orthogonal polynomials. They are orthogonal with respect to the weight (+) on the interval [,]. The Gegenbauer polynomials, and thus also the Legendre, Zernike and Chebyshev polynomials, are special cases of the Jacobi polynomials. [1]
Chihara, Theodore Seio (2001), "45 years of orthogonal polynomials: a view from the wings", Proceedings of the Fifth International Symposium on Orthogonal Polynomials, Special Functions and their Applications (Patras, 1999), Journal of Computational and Applied Mathematics, 133 (1): 13– 21, doi: 10.1016/S0377-0427(00)00632-4, ISSN 0377-0427 ...
Biorthogonal polynomials are a generalization of orthogonal polynomials and share many of their properties. There are two different concepts of biorthogonal polynomials in the literature: Iserles & Nørsett (1988) introduced the concept of polynomials biorthogonal with respect to a sequence of measures, while Szegő introduced the concept of ...