This function is an implementation of Koepf's extension of Zeilberger's algorithm, calculating a (downward) recurrence equation for the sum

the sum to be taken over all integers k, with respect to n. Here, U and L denote the lists of upper and lower parameters, and z is the evaluation point. The arguments of U and L are assumed to be rational-linear with respect to n. The resulting expression equals zero.

The output is a recurrence which equals zero. The recurrence is output as a function of n, the recurrence variable, and .

The command with(sumtools,hyperrecursion) allows the use of the abbreviated form of this command.