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meromorphic

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Definitions of meromorphic in various dictionaries:

MEROMORPHIC - In the mathematical field of complex analysis, a meromorphic function on an open subset D of the complex plane is a function that is holomorphic on a...

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which is a ratio of two holomorphic functions.

Meromorphic might refer to
In the mathematical field of complex analysis, a Meromorphic function on an open subset D of the complex plane is a function that is holomorphic on all of D except for a discrete set of isolated points, which are poles of the function. This terminology comes from the Ancient Greek meros (), meaning "part," as opposed to holos (), meaning "whole." * Every meromorphic function on D can be expressed as the ratio between two holomorphic functions (with the denominator not constant 0) defined on D: any pole must coincide with a zero of the denominator.* 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 multiplicities of these zeros. * From an algebraic point of

Meromorphic might refer to

In the mathematical field of complex analysis, a Meromorphic function on an open subset D of the complex plane is a function that is holomorphic on all of D except for a discrete set of isolated points, which are poles of the function. This terminology comes from the Ancient Greek meros (), meaning "part," as opposed to holos (), meaning "whole."
* Every meromorphic function on D can be expressed as the ratio between two holomorphic functions (with the denominator not constant 0) defined on D: any pole must coincide with a zero of the denominator.* 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 multiplicities of these zeros.
* From an algebraic point of

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