Let be an th degree Polynomial with zeros at , ..., . Then the fundamental
Polynomials are

(1) |

(2) |

(3) | |||

(4) | |||

(5) | |||

(6) |

for , 2, ..., . Now let , ..., and , ..., be values. Then the expansion

(7) |

(8) | |||

(9) |

If , these are called Step Polynomials. The fundamental polynomials satisfy

(10) |

(11) |

(12) | |||

(13) | |||

(14) | |||

(15) | |||

(16) | |||

(17) |

where are Christoffel Numbers.

**References**

Hildebrand, F. B. *Introduction to Numerical Analysis.* New York: McGraw-Hill, pp. 314-319, 1956.

Szegö, G. *Orthogonal Polynomials, 4th ed.* Providence, RI: Amer. Math. Soc., pp. 330-332, 1975.

© 1996-9

1999-05-25