# Gegenbauer polynomials

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## Gegenbauer polynomials

[′gāg·ən‚bau̇r ‚päl·i′nō·mē·əlz]
(mathematics)
A family of polynomials solving a special case of the Gauss hypergeometric equation. Also known as ultraspherical polynomials.
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Author Brian George Spencer Doman examines classical orthogonal polynomials and their additional properties, covering hermite polynomials, associated Laguerre polynomials, Legendre polynomials, Chebyshev polynomials, Gegenbauer polynomials, associated Legendre functions, Jacobi polynomials, and many other related mathematical subjects over twelve chapters and appendices.
Gegenbauer polynomials or ultraspherical polynomials [C.
This can be done for the unispherical windows [3] based on Gegenbauer polynomials as well as for windows proposed by Zierhofer [4].
For a given positive integer number N, the orthogonality of the generalized Gegenbauer polynomials [{[C.
Stieltjes interlacing was studied for the zeros of polynomials from different sequences of one-parameter orthogonal families, namely, Gegenbauer polynomials [C.
Key words and phrases : Gibbs phenomenon, Gegenbauer polynomials, spherical harmonics, edge detection.
This family of windows is based on Gegenbauer polynomials [7], being the generalization of Legendre polynomials and the special cases of Jacobi polynomials.
Generalizations of the classical Gegenbauer polynomials to the Clifford analysis framework are called Clifford-Gegenbauer polynomials and were introduced as well on the closed unit ball B(1) (see [4]), as on the Euclidean space [R.
This also holds for Gegenbauer polynomials where sines and cosines (in this order) are included in the form of Chebyshev polynomials of second and first kind.
n] have been obtained for the Gegenbauer polynomials with index [lambda] = 0 (Chebyshev), [lambda] = 1 (Chebyshev of the second kind) and [lambda] = 2 only.
n] is the Gegenbauer polynomial of degree n and [V.

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