Indefinite product

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In mathematics, the indefinite product operator is the inverse operator of . It is like a discrete version of the indefinite product integral. Some authors use term discrete multiplicative integration[1]

Thus

More explicitly, if , 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[edit]

If is a period of function then

Connection to indefinite sum[edit]

Indefinite product can be expressed in terms of indefinite sum:

Alternative usage[edit]

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.[2] e.g.

.

Rules[edit]

List of indefinite products[edit]

This is a list of indefinite products . Not all functions have an indefinite product which can be expressed in elementary functions.

(see K-function)
(see Barnes G-function)
(see super-exponential function)

See also[edit]

References[edit]

Further reading[edit]