A hypergeometric series is a series for which and the ratio of consecutive terms is a Rational
Function of the summation index , i.e., one for which

(1) |

(2) |

(3) |

Many sums can be written as Generalized Hypergeometric Functions by inspections of the ratios of consecutive terms in the generating hypergeometric series.

**References**

Petkovsek, M.; Wilf, H. S.; and Zeilberger, D. ``Hypergeometric Series,'' ``How to Identify a Series as Hypergeometric,''
and ``Software That Identifies Hypergeometric Series.'' §3.2-3.4 in *A=B.*
Wellesley, MA: A. K. Peters, pp. 34-42, 1996.

© 1996-9

1999-05-25