meromorphic function
mathematics
Quick Summary
A meromorphic function is a complex-variable function that is analytic (can be differentiated) everywhere in a region except for isolated singularities. At these singularities, the function's value approaches infinity. Each singularity is contained within a neighborhood where the function is analytic, apart from the singular point itself.1
The Riemann zeta function, for example, is a meromorphic function. It has a pole (a type of isolated singularity) at z = 1, where the series diverges to infinity.2
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