For a specified hyperexponential function  of x and y, the Zeilberger(F, x, y, Dx) calling sequence constructs for  a Z-pair  that consists of a linear differential operator with coefficients that are polynomials of x over the complex number field

and a hyperexponential function  of x and y such that

Dx and Dy are the differential operators with respect to x, and y, respectively, defined by , and .

By assigning values to the global variables _MINORDER and _MAXORDER, the algorithm is restricted to finding a Z-pair  for  such that the order of L is between _MINORDER and _MAXORDER.

The algorithm has two implementations. The default implementation uses a variant of Gosper's algorithm, and another one is based on the universal denominators. With the 'gosper_free' option, Gosper-free implementation is used.

The output from the Zeilberger command is a list of two elements  representing the computed Z-pair .

Almkvist, G, and Zeilberger, D. "The method of differentiating under the integral sign." Journal of Symbolic Computation. Vol. 10. (1990): 571-591.