scipy.special.roots_genlaguerre¶
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scipy.special.roots_genlaguerre(n, alpha, mu=False)[source]¶ Gauss-generalized Laguerre quadrature.
Computes the sample points and weights for Gauss-generalized Laguerre quadrature. The sample points are the roots of the n-th degree generalized Laguerre polynomial, \(L^{\alpha}_n(x)\). These sample points and weights correctly integrate polynomials of degree \(2n - 1\) or less over the interval \([0, \infty]\) with weight function \(f(x) = x^{\alpha} e^{-x}\).
- Parameters
- nint
quadrature order
- alphafloat
alpha must be > -1
- mubool, optional
If True, return the sum of the weights, optional.
- Returns
- xndarray
Sample points
- wndarray
Weights
- mufloat
Sum of the weights