In this paper a general method is presented from which one can obtain a wide class of combinatorial identities. The following is the main result. Let , be any nonnegative integers, and let be given by
where and are functions defined on . Let and be any two sequences, and let , be the corresponding ordinary generating functions. Then
where denotes the th derivative with regard to .
The above result is generalized to functions represented by integrals over a real -dimensional domain. Numerous examples illustrating the use of these two results are also given.