Indefinite product
In mathematics, the indefinite product operator is the inverse operator of formula_1. It is a discrete version of the geometric integral of geometric calculus, one of the non-Newtonian calculi. Some authors use term discrete multiplicative integration. Thus More explicitly, if formula_3, then If "F"("x") is a solution of this functional equation for a given "f"("x"), then so is "CF"("x") for any constant "C". Therefore, each indefinite product actually represents a family of functions, differing by a multiplicative constant. Period rule. If formula_5 is a period of function formula_6 then Connection to indefinite sum. Indefinite product can be  expressed in terms of indefinite sum: Alternative usage. Some authors use the phrase "indefinite product" in a slightly different but related way to describe a product in which the numerical value of the upper limit is not given. e.g. List of indefinite products. This is a list of indefinite products formula_13. Not all functions have an indefinite product which can be expressed in elementary functions.