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.
See also
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 \(\alpha = 0\).