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# Multiplicity

The word multiplicity is a general term meaning "the number of values for which a given condition holds." For example, the term is used to refer to the value of the totient valence function or the number of times a given polynomial equation has a root at a given point.

Let be a root of a function , and let be the least positive integer such that . Then the power series of about begins with the th term,

and is said to have a root of multiplicity (or "order") . If , the root is called a simple root (Krantz 1999, p. 70).

Degenerate, Module Multiplicity, Multiple Root, Noether's Fundamental Theorem, Root, Simple Root, Totient Valence Function

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## References

Krantz, S. G. "Zero of Order n." §5.1.3 in Handbook of Complex Variables. Boston, MA: Birkhäuser, p. 70, 1999.

Multiplicity

## Cite this as:

Weisstein, Eric W. "Multiplicity." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/Multiplicity.html