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

nint

Degree of the polynomial.

monicbool, optional

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

Returns

Porthopoly1d

Shifted Legendre polynomial.

Notes

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