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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.