The early history of the factorial function

was encountered in the evaluation of integrals, in the summation of series, in number theory, eie. Indeed the function is probably the most frequently used of the higher transcendental functions in applications. From about the mid-seventeenth to the early nineteenth century, the factorial function was intensively studied by some of the foremost mathematicians of the period, and its basic properties were determined. The purpose of this paper is to give a connected account of these developments. In some cases the original notation has been modernized, and original proofs have been replaced by simpler or more direct demonstrations. Treatises on the factorial function which contain material and references on its early history were written by G. Brunel [1] and N. Nielsen [1].