The IsProperHypergeometricTerm(T,n,k) command returns true if  is a proper hypergeometric term. Otherwise, it returns false.

The IsHolonomic(T,n,k) command returns true if the bivariate hypergeometric term  is holonomic. Otherwise, it returns false.

A bivariate hypergeometric term  is proper if it can be written as  where  is a polynomial of n and k, and ,  are integers, and  are non-negative integers,  are complex numbers.

It can be shown that  is proper if and only if it is holonomic.

Note: If  is a proper hypergeometric term, the termination of Zeilberger's algorithm is guaranteed.

Abramov, S.A., and Petkovsek, M. "Proof of a Conjecture of Wilf and Zeilberger." Preprint series. Vol. 39. (2001): 748. University of Ljubljana, ISSN 1318--4865.