scipy.special.eval_sh_legendre¶

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

Evaluate shifted Legendre polynomial at a point.

These polynomials are defined as

$P_n^*(x) = P_n(2x - 1)$

where $$P_n$$ is a Legendre polynomial. See 2.2.11 in [AS] for details.

Parameters
narray_like

Degree of the polynomial. If not an integer, the value is determined via the relation to eval_legendre.

xarray_like

Points at which to evaluate the shifted Legendre polynomial

Returns
Pndarray

Values of the shifted Legendre polynomial

roots_sh_legendre

roots and quadrature weights of shifted Legendre polynomials

sh_legendre

shifted Legendre polynomial object

eval_legendre

evaluate Legendre polynomials

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.