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Indefinite product

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In mathematics, the indefinite product operator is the inverse operator of . It is a discrete version of the geometric integral of geometric calculus, one of the non-Newtonian calculi.

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

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If is a period of function then

Connection to indefinite sum

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Indefinite product can be expressed in terms of indefinite sum:

Alternative usage

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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.[1] e.g.

.

Rules

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List of indefinite products

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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

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References

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Further reading

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