Corollary 6.1.  Let  [Graphics:Images/CauchyGoursatMod_gr_41.gif]  denote a fixed complex value.  If C is a simple closed contour with positive orientation such that  [Graphics:Images/CauchyGoursatMod_gr_42.gif]  lies interior to C, then

(i)                  [Graphics:Images/CauchyGoursatMod_gr_43.gif],   and  

(ii)                 [Graphics:Images/CauchyGoursatMod_gr_44.gif],   where n is any integer except [Graphics:Images/CauchyGoursatMod_gr_45.gif].  

Proof.

Proof of Corollary 6.1 is in the book.

 

Complex Analysis for Mathematics and Engineering