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  

Demonstration for (i).

(a)   Show that [Graphics:../Images/CauchyGoursatMod_gr_46.gif].  
For illustration.  We use a circle of radius 1 centered at  [Graphics:../Images/CauchyGoursatMod_gr_47.gif].  

[Graphics:../Images/CauchyGoursatMod_gr_48.gif]





[Graphics:../Images/CauchyGoursatMod_gr_49.gif]

[Graphics:../Images/CauchyGoursatMod_gr_50.gif]

[Graphics:../Images/CauchyGoursatMod_gr_51.gif]

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

(c) 2006 John H. Mathews, Russell W. Howell