scipy.special.genlaguerre¶

scipy.special.genlaguerre(n, alpha, monic=False)[source]

Generalized (associated) Laguerre polynomial.

Defined to be the solution of

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

where $$\alpha > -1$$; $$L_n^{(\alpha)}$$ is a polynomial of degree $$n$$.

Parameters
nint

Degree of the polynomial.

alphafloat

Parameter, must be greater than -1.

monicbool, optional

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

Returns
Lorthopoly1d

Generalized Laguerre polynomial.

laguerre

Laguerre polynomial.

Notes

For fixed $$\alpha$$, the polynomials $$L_n^{(\alpha)}$$ are orthogonal over $$[0, \infty)$$ with weight function $$e^{-x}x^\alpha$$.

The Laguerre polynomials are the special case where $$\alpha = 0$$.

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