# A Theorem concerning Meromorphic Functions, complex analysis.

Is there a theorem in complex analysis which says something along the lines that,

If two meromorphic function have same set of poles then they are same. I mean to say that, given a set of poles $$M=\{z_1,z_2,\dots,z_n\}$$, there is a unique meromorphic function having poles at $$z_1,z_2,\dots,z_n$$

If there is such theorem, I request you to mention books/online source where I can find the proof.

• – lhf Oct 23 '18 at 12:56

If $$f$$ is a meromorphic function and $$g$$ is an entire function without zeros, then $$fg$$ is a meromorphic function with exactly the same poles as $$f$$.