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

outndarray, optional

Optional output array for the function values

Returns

Pscalar or ndarray

Values of the shifted Legendre polynomial

See also

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.