sh_legendre — SciPy v1.15.2 Manual (original) (raw)

scipy.special.

scipy.special.sh_legendre(n, monic=False)[source]#

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.