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

(1) |

(2) |

(3) |

(4) |

(5) |

(6) |

(7) |

(8) | |||

(9) |

where

(10) |

(11) |

(12) |

2 | ± 0.707107 | 1.5708 |

3 | 0 | 1.0472 |

± 0.866025 | 1.0472 | |

4 | ± 0.382683 | 0.785398 |

± 0.92388 | 0.785398 | |

5 | 0 | 0.628319 |

± 0.587785 | 0.628319 | |

± 0.951057 | 0.628319 |

**References**

Hildebrand, F. B. *Introduction to Numerical Analysis.* New York: McGraw-Hill, pp. 330-331, 1956.

© 1996-9

1999-05-26