In mathematics, Gegenbauer polynomials or ultraspherical polynomials C(α) n(x) are orthogonal polynomials on the interval [−1,1] with respect to the weight...

1]} . The Gegenbauer polynomials, and thus also the Legendre, Zernike and Chebyshev polynomials, are special cases of the Jacobi polynomials. The Jacobi...

The Gegenbauer polynomials form the most important class of Jacobi polynomials; they include the Chebyshev polynomials, and the Legendre polynomials as...

polynomials (including as a special case the Gegenbauer polynomials, Chebyshev polynomials, and Legendre polynomials). They have many important applications...

mathematics, Legendre polynomials, named after Adrien-Marie Legendre (1782), are a system of complete and orthogonal polynomials with a wide number of...

mathematician remembered best as an algebraist. Gegenbauer polynomials are named after him. Leopold Gegenbauer was the son of a doctor. He studied at the University...

The Chebyshev polynomials are two sequences of orthogonal polynomials related to the cosine and sine functions, notated as T n ( x ) {\displaystyle T_{n}(x)}...

Ehrhart polynomial Exponential polynomials Favard's theorem Fibonacci polynomials Gegenbauer polynomials Hahn polynomials Hall–Littlewood polynomials Heat...

case α = β turns Jacobi polynomials into Gegenbauer polynomials, in which case the technique is sometimes called Gauss–Gegenbauer quadrature. Gauss–Jacobi...

painter Leopold Gegenbauer (1849–1903), Austrian mathematician Carl Gegenbaur (1826–1903), German anatomist and professor Gegenbauer polynomials, in mathematics...

harmonic polynomials  R 3 → C  that are homogeneous of degree  ℓ } . {\displaystyle \mathbf {A} _{\ell }=\left\{{\text{harmonic polynomials }}\mathbb...

equation for this potential can be described analytically with Gegenbauer polynomials. As v {\displaystyle v} passes through each of these values, a manifold...

equation for this potential can be described analytically with Gegenbauer polynomials. As v {\displaystyle v} passes through each of these values, a manifold...

Gaussian polynomial, Gaussian distribution, Hypergeometric function 2F1, etc. Leopold Bernhard Gegenbauer: Gegenbauer polynomials Gottlieb polynomial Gould...

where C N α ( x ) {\displaystyle C_{N}^{\alpha }(x)} denotes a Gegenbauer polynomial and p {\displaystyle p} is in units of ℏ / a 0 ∗ {\displaystyle...

orthogonal polynomials, including Jacobi polynomials P(α,β) n and their special cases Legendre polynomials, Chebyshev polynomials, Gegenbauer polynomials, Zernike...

Classical orthogonal polynomials Hermite polynomials Laguerre polynomials Jacobi polynomials Gegenbauer polynomials Legendre polynomials Euclidean space Metric...

the Neumann polynomials, introduced by Carl Neumann for the special case α = 0 {\displaystyle \alpha =0} , are a sequence of polynomials in 1 / t {\displaystyle...

Chandrasekhar. The initial conditions can be expressed in terms of Gegenbauer polynomials (without loss of generality), Q 1 ( r , μ , 0 ) = ∑ n = 0 ∞ q 2...

method expands the field equations into polynomial functions such as Gegenbauer polynomials or Chebyshev polynomials. These methods can be mixed according...

formula (formerly called the Ivory–Jacobi formula) generates the Legendre polynomials. It was independently introduced by Olinde Rodrigues (1816), Sir James...

{\displaystyle {\mathcal {G}}_{n}^{\ell +1}(\cos \chi )} are the Gegenbauer polynomials. Changing in (10) variables as one observes that the ψ K ℓ ( χ )...

distance, in cosmology P {\displaystyle \mathrm {P} } represents: one of the Gegenbauer functions in analytic number theory (may be replaced by the capital form...

Crstici (2004) p.106 Holden et al in external links. The formula is Gegenbauer's. All of these formulas are from Andrica and Piticari in #External links...

Jordan's totient function Holden et al. in external links The formula is Gegenbauer's Hardy & Wright, Thm. 288–290 Dineva in external links, prop. 4 Hardy...