- legendres :: [Poly Rational]
- legendre :: Fractional a => Int -> Poly a
- evalLegendre :: Fractional a => Int -> a -> a
- evalLegendres :: Fractional a => a -> [a]
- evalLegendreDeriv :: Fractional a => Int -> a -> (a, a)
- legendreRoots :: (Fractional b, Ord b) => Int -> b -> [b]

# Documentation

legendres :: [Poly Rational]Source

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 => Int -> Poly aSource

Compute the coefficients of the n'th Legendre polynomial.

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

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]Source

Evaluate all the Legendre polynomials at a point X.

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

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]Source

Zeroes of the n'th Legendre polynomial.