This function is an implementation of Zeilberger-Koepf's algorithm, and calculates a closed form for the sum

the sum to be taken over all integers k, with respect to n, whenever an extension of Zeilberger's algorithm gives a suitable recurrence equation. 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 procedure Hypersum is the corresponding inert form which remains unevaluated.

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