Meromorphic functions

Meromorphic function

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 set of isolated points, which are poles of the function. The term comes from the Ancient Greek meros (μέρος), meaning "part". 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. (Wikipedia).

Meromorphic function
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Field of fractions | Integral domain | Biholomorphism | Accumulation point | Rational function | Complex analysis | Cousin problems | Isolated point | Mittag-Leffler's theorem | Complex manifold | Riemann sphere | Weierstrass factorization theorem | Rational number | Endomorphism | Complex logarithm | Field extension | Complex plane | Riemann surface | Gamma function | Connected space | Function (mathematics) | Field (mathematics) | Integer | Removable singularity | Multiplicity (mathematics) | Group theory | Codimension | Holomorphic function | Analytic continuation | Complex torus | Essential singularity | Riemann zeta function | Open set