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)
Famous quotes containing the words multiplicity of and/or multiplicity:
“The point of cities is multiplicity of choice.”
—Jane Jacobs (b. 1916)
“One might get the impression that I recommend a new methodology which replaces induction by counterinduction and uses a multiplicity of theories, metaphysical views, fairy tales, instead of the customary pair theory/observation. This impression would certainly be mistaken. My intention is not to replace one set of general rules by another such set: my intention is rather to convince the reader that all methodologies, even the most obvious ones, have their limits.”
—Paul Feyerabend (1924–1994)