scipy.special.sh_legendre

scipy.special.sh_legendre(n, monic=False)

Shifted Legendre polynomial.

Defined as \(P^*_n(x) = P_n(2x - 1)\) for \(P_n\) the nth Legendre polynomial.

Parameters:

n : int

Degree of the polynomial.

monic : bool, optional

If True, scale the leading coefficient to be 1. Default is False.

Returns:

P : orthopoly1d

Shifted Legendre polynomial.

Notes

The polynomials \(P^*_n\) are orthogonal over \([0, 1]\) with weight function 1.