This paper discusses and evaluates the standard procedures available in Maple 4.3 for handling hypergeometric series. Some suggestions for improvement are given. The paper concludes with a survey of the algorithms of Gosper and of Zeilberger for possibly evaluating a terminating series of hypergeometric type. This paper appeared in Orthogonal polynomials and their applications, C. Brezinski, L....

The number of ways of placing k non-attacking rooks on a Ferrers board is expressed as a hypergeometric series, of a type originally studied by Karlsson and Minton. Known transformation identities for series of this type translate into new theorems about rook polynomials.