Data.Poly.Orthogonal

Classical orthogonal polynomials.

Documentation

legendre :: (Eq a, Field a, Vector v a) => [Poly v a]

Legendre polynomials.

>>> take 3 legendre :: [Data.Poly.VPoly Double]
[1.0,1.0 * X + 0.0,1.5 * X^2 + 0.0 * X + (-0.5)]

legendreShifted :: (Eq a, Euclidean a, Ring a, Vector v a) => [Poly v a]

Shifted Legendre polynomials.

>>> take 3 legendreShifted :: [Data.Poly.VPoly Integer]
[1,2 * X + (-1),6 * X^2 + (-6) * X + 1]

gegenbauer :: (Eq a, Field a, Vector v a) => a -> [Poly v a]

Gegenbauer polynomials.

jacobi :: (Eq a, Field a, Vector v a) => a -> a -> [Poly v a]

Jacobi polynomials.

chebyshev1 :: (Eq a, Ring a, Vector v a) => [Poly v a]

Chebyshev polynomials of the first kind.

>>> take 3 chebyshev1 :: [VPoly Integer]
[1,1 * X + 0,2 * X^2 + 0 * X + (-1)]

chebyshev2 :: (Eq a, Ring a, Vector v a) => [Poly v a]

Chebyshev polynomials of the second kind.

>>> take 3 chebyshev2 :: [VPoly Integer]
[1,2 * X + 0,4 * X^2 + 0 * X + (-1)]

hermiteProb :: (Eq a, Ring a, Vector v a) => [Poly v a]

Probabilists' Hermite polynomials.

>>> take 3 hermiteProb :: [VPoly Integer]
[1,1 * X + 0,1 * X^2 + 0 * X + (-1)]

hermitePhys :: (Eq a, Ring a, Vector v a) => [Poly v a]

Physicists' Hermite polynomials.

>>> take 3 hermitePhys :: [VPoly Double]
[1.0,2.0 * X + 0.0,4.0 * X^2 + 0.0 * X + (-2.0)]

laguerre :: (Eq a, Field a, Vector v a) => [Poly v a]

Laguerre polynomials.

>>> take 3 laguerre :: [VPoly Double]
[1.0,(-1.0) * X + 1.0,0.5 * X^2 + (-2.0) * X + 1.0]

laguerreGen :: (Eq a, Field a, Vector v a) => a -> [Poly v a]

Generalized Laguerre polynomials