Corollary 7.5.  If f(z) is analytic and has a zero of order k at the point  [Graphics:Images/SingularityZeroPoleMod._gr_328.gif],  then  [Graphics:Images/SingularityZeroPoleMod._gr_329.gif]  has a pole of order k at  [Graphics:Images/SingularityZeroPoleMod._gr_330.gif].  

Proof.

Proof of Corollary 7.5 is an exercise in the book.

 

Complex Analysis for Mathematics and Engineering