Meromorphic function: Difference between revisions

Revision as of 01:38, 6 January 2020

Revision as of 21:33, 17 January 2020

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Intuitively, a meromorphic function is a ratio of two well-behaved (holomorphic) functions. Such a function will still be well-behaved, except possibly at the points where the denominator of the fraction is zero. If the denominator has a zero at ''z'' and the numerator does not, then the value of the function will approach infinity; if both parts have a zero at ''z'', then one must compare the [[Multiplicity (mathematics)#Multiplicity of a root of a polynomial|multiplicity]] of these zeros.

From an algebraic point of view, if the functionsfunction's ___domain is [[connected set|connected]], then the set of meromorphic functions is the [[field of fractions]] of the [[integral ___domain]] of the set of holomorphic functions. This is analogous to the relationship between the [[rational number]]s and the [[integer]]s.

==Prior, alternate use==