Let  be a hypergeometric term of m and k. Let  where b and d are integers. The ExtendedZeilberger(V, n, k, En) command, an extension to Zeilberger's algorithm, constructs the minimal Z-pair for  provided that it exists.

It can be shown that a Z-pair for  exists if and only if a Z-pair for the hypergeometric term  exists.

Le, H.Q. "Computing the Minimal Telescoper for Sums of Hypergeometric Terms." SIGSAM Bulletin: Communications on Computer Algebra. Vol. 35 No. 3. (2001): 2-10.