1
$\begingroup$

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.

$\endgroup$
1
$\begingroup$

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 $f$.

The relevant uniqueness theorem is the Weierstrass factorization theorem.

See also the Mittag-Leffler's theorem.

$\endgroup$
  • $\begingroup$ Thank you. This is exactly I was looking for! $\endgroup$ – StammeringMathematician Oct 23 '18 at 12:54

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.