Multiplicity of A Zero
A complex number a is a simple zero of f, or a zero of multiplicity 1 of f, if f can be written as
where g is a holomorphic function g such that g(a) is not zero.
Generally, the multiplicity of the zero of f at a is the positive integer n for which there is a holomorphic function g such that
The multiplicity of a zero a is also known as the order of vanishing of the function at a.
Read more about this topic: Zero (complex Analysis)
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