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).
