SciPy

scipy.special.eval_legendre

scipy.special.eval_legendre(n, x, out=None) = <ufunc 'eval_legendre'>

Evaluate Legendre polynomial at a point.

The Legendre polynomials can be defined via the Gauss hypergeometric function \({}_2F_1\) as

\[P_n(x) = {}_2F_1(-n, n + 1; 1; (1 - x)/2).\]

When \(n\) is an integer the result is a polynomial of degree \(n\).

Parameters:

n : array_like

Degree of the polynomial. If not an integer, the result is determined via the relation to the Gauss hypergeometric function.

x : array_like

Points at which to evaluate the Legendre polynomial

Returns:

P : ndarray

Values of the Legendre polynomial

See also

p_roots
roots and quadrature weights of Legendre polynomials
legendre
Legendre polynomial object
hyp2f1
Gauss hypergeometric function
numpy.polynomial.legendre.Legendre
Legendre series