Gauss–Laguerre quadrature

In numerical analysis Gauss–Laguerre quadrature (named after Carl Friedrich Gauss and Edmond Laguerre) is an extension of the Gaussian quadrature method for approximating the value of integrals of the following kind: ∫ 0 ∞ e − x f ( x ) d x . {\displaystyle \int _{0}^{\infty }e^{-x}f(x)\,dx.} In this case ∫ 0 ∞ e − x f ( x ) d x ≈ ∑ i = 1 n w i f ( x i ) {\displaystyle \int _{0}^{\infty }e^{-x}f(x)\,dx\approx \sum _{i=1}^{n}w_{i}f(x_{i})} where xi is the i-th root of Laguerre polynomial Ln(x) and the weight wi is given by w i = x i ( n + 1 ) 2 [ L n + 1 ( x i ) ] 2 .

Source: Wikipedia — Gauss–Laguerre quadrature (CC BY-SA 4.0)

Gauss–Laguerre quadrature

In numerical analysis Gauss–Laguerre quadrature (named after Carl Friedrich Gauss and Edmond Laguerre) is an extension of the Gaussian quadrature method for approximating the value of integrals of the following kind: ∫ 0 ∞ e − x f ( x ) d x . {\displaystyle \int _{0}^{\infty }e^{-x}f(x)\,dx.} In this case ∫ 0 ∞ e − x f ( x ) d x ≈ ∑ i = 1 n w i f ( x i ) {\displaystyle \int _{0}^{\infty }e^{-x}f(x)\,dx\approx \sum _{i=1}^{n}w_{i}f(x_{i})} where xi is the i-th root of Laguerre polynomial Ln(x) and the weight wi is given by w i = x i ( n + 1 ) 2 [ L n + 1 ( x i ) ] 2 .

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Source: Wikipedia "Gauss–Laguerre quadrature" · CC BY-SA 4.0

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