Also called Gauss-Laguerre Quadrature or Laguerre Quadrature. A Gaussian Quadrature over
the interval with Weighting Function . The Abscissas for quadrature order are
given by the Roots of the Laguerre Polynomials . The weights are

(1) |

(2) |

(3) |

(4) |

(5) |

(6) |

(7) |

(8) |

(9) |

Beyer (1987) gives a table of Abscissas and weights up to .

2 | 0.585786 | 0.853553 |

3.41421 | 0.146447 | |

3 | 0.415775 | 0.711093 |

2.29428 | 0.278518 | |

6.28995 | 0.0103893 | |

4 | 0.322548 | 0.603154 |

1.74576 | 0.357419 | |

4.53662 | 0.0388879 | |

9.39507 | 0.000539295 | |

5 | 0.26356 | 0.521756 |

1.4134 | 0.398667 | |

3.59643 | 0.0759424 | |

7.08581 | 0.00361176 | |

12.6408 | 0.00002337 |

The Abscissas and weights can be computed analytically for small .

2 | ||

For the associated Laguerre polynomial with Weighting Function
,

(10) |

(11) |

(12) |

(13) |

**References**

Beyer, W. H. *CRC Standard Mathematical Tables, 28th ed.* Boca Raton, FL: CRC Press, p. 463, 1987.

Chandrasekhar, S. *Radiative Transfer.* New York: Dover, pp. 64-65, 1960.

Hildebrand, F. B. *Introduction to Numerical Analysis.* New York: McGraw-Hill, pp. 325-327, 1956.

© 1996-9

1999-05-26