multiplicative function

The Legendre symbol is a completely multiplicative function of its top argument:

This is a time based model that describes the probability of a system operator's failure as a multiplicative function of 5 main factors.

Totally additive is also used in this sense by analogy with totally multiplicative functions.

A multiplicative function modeled after this phenomenon was created.

Many specific examples are given in the article on multiplicative functions.

Completely multiplicative functions also satisfy a pseudo-associative law.

Outside number theory, the term multiplicative function is usually used for completely multiplicative functions.

Some multiplicative functions are defined to make formulas easier to write:

With this operation, the set of all multiplicative functions turns into an abelian group; the identity element is .

Relations among the multiplicative functions discussed above include: