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scipy.special.laguerre

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

Laguerre polynomial.

Defined to be the solution of

$$x\frac{d^2}{dx^2}L_n + (1 - x)\frac{d}{dx}L_n + nL_n = 0;$$

$L_n$ is a polynomial of degree $n$.

Parameters:

n : int

Degree of the polynomial.

monic : bool, optional

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

Returns:

L : orthopoly1d

Laguerre Polynomial.

Notes

The polynomials $L_n$ are orthogonal over $[0, \infty)$ with weight function $e^{-x}$.