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
If is a period of function 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.[2] e.g.
- .
Rules
List of indefinite products
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
References
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Further reading