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 \(n\). See 22.5.49 in [AS] for details.
- Parameters
- narray_like
Degree of the polynomial. If not an integer, the result is determined via the relation to the Gauss hypergeometric function.
- xarray_like
Points at which to evaluate the Legendre polynomial
- Returns
- Pndarray
Values of the Legendre polynomial
See also
roots_legendre
roots and quadrature weights of Legendre polynomials
legendre
Legendre polynomial object
hyp2f1
Gauss hypergeometric function
numpy.polynomial.legendre.Legendre
Legendre series
References
- AS
Milton Abramowitz and Irene A. Stegun, eds. Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables. New York: Dover, 1972.