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Closed Form

A discrete Function $A(n,k)$ is called closed form (or sometimes ``hypergeometric'') in two variables if the ratios $A(n+1,k)/A(n,k)$ and $A(n,k+1)/A(n,k)$ are both Rational Functions. A pair of closed form functions $(F,G)$ is said to be a Wilf-Zeilberger Pair if


See also Rational Function, Wilf-Zeilberger Pair


Petkovsek, M.; Wilf, H. S.; and Zeilberger, D. A=B. Wellesley, MA: A. K. Peters, p. 141, 1996.

Zeilberger, D. ``Closed Form (Pun Intended!).'' Contemporary Math. 143, 579-607, 1993.

© 1996-9 Eric W. Weisstein