Math.Polynomial.Legendre

Documentation

legendres :: [Poly Rational]

The Legendre polynomials with Rational coefficients. These polynomials form an orthogonal basis of the space of all polynomials, relative to the L2 inner product on [-1,1] (which is given by integrating the product of 2 polynomials over that range).

legendre :: (Fractional a, Eq a) => Int -> Poly a

Compute the coefficients of the n'th Legendre polynomial.

evalLegendre :: Fractional a => Int -> a -> a

Evaluate the n'th Legendre polynomial at a point X. Both more efficient and more numerically stable than computing the coefficients and evaluating the polynomial.

evalLegendres :: Fractional a => a -> [a]

Evaluate all the Legendre polynomials at a point X.

evalLegendreDeriv :: Fractional a => Int -> a -> (a, a)

Evaluate the n'th Legendre polynomial and its derivative at a point X. Both more efficient and more numerically stable than computing the coefficients and evaluating the polynomial.

legendreRoots :: (Fractional b, Ord b) => Int -> b -> [b]

Zeroes of the n'th Legendre polynomial.