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What (who) is Gegenbauer polynomials - definition
Gegenbauer polynomials
(x) with n=10 and m=1 in the complex plane from -2-2i to 2+2i with colors created with Mathematica 13.1 function ComplexPlot3D.svg?width=200 "Plot of the Gegenbauer polynomial C n^(m)(x) with n=10 and m=1 in the complex plane from -2-2i to 2+2i with colors created with Mathematica 13.1 function ComplexPlot3D")
ORTHOGAL POLYNOMIAL SEQUENCE ON THE INTERVAL [−1,1] WITH RESPECT TO THE WEIGHT FUNCTION (1−𝑥²)^{𝛼−½}
Gegenbauer polynomial; Ultraspherical polynomials; Gegenbauer function; Ultraspherical polynomial; Gegenbauer Polynomials; Ultraspherical differential equation; Ultraspherical function
In mathematics, Gegenbauer polynomials or ultraspherical polynomials C(x) are orthogonal polynomials on the interval [−1,1] with respect to the weight function (1 − x2)α–1/2. They generalize Legendre polynomials and Chebyshev polynomials, and are special cases of Jacobi polynomials.
Leopold Gegenbauer
AUSTRIAN MATHEMATICIAN
Leopold Bernhard Gegenbauer
Leopold Bernhard Gegenbauer (2 February 1849, Asperhofen – 3 June 1903, Gießhübl) was an Austrian mathematician remembered best as an algebraist. Gegenbauer polynomials are named after him.
Bateman polynomials
In mathematics, the Bateman polynomials are a family Fn of orthogonal polynomials introduced by . The Bateman–Pasternack polynomials are a generalization introduced by .
