Also called Hermite Quadrature. A Gaussian Quadrature over the interval
with
Weighting Function . The Abscissas for quadrature order are given by the
roots of the Hermite Polynomials , which occur symmetrically about 0. The
Weights are

(1) |

(2) |

(3) |

(4) |

(5) |

Using the Recurrence Relation

(6) |

(7) |

(8) |

(9) |

2 | ± 0.707107 | 0.886227 |

3 | 0 | 1.18164 |

± 1.22474 | 0.295409 | |

4 | ± 0.524648 | 0.804914 |

± 1.65068 | 0.0813128 | |

5 | 0 | 0.945309 |

± 0.958572 | 0.393619 | |

± 2.02018 | 0.0199532 |

The Abscissas and weights can be computed analytically for small .

2 | ||

3 | 0 | |

4 | ||

**References**

Beyer, W. H. *CRC Standard Mathematical Tables, 28th ed.* Boca Raton, FL: CRC Press, p. 464, 1987.

Hildebrand, F. B. *Introduction to Numerical Analysis.* New York: McGraw-Hill, pp. 327-330, 1956.

© 1996-9

1999-05-25