Example 3.3.  If we use Equation (3-12) with  [Graphics:Images/AnalyticFunctionMod_gr_126.gif],  and  [Graphics:Images/AnalyticFunctionMod_gr_127.gif],  then we get  

            [Graphics:Images/AnalyticFunctionMod_gr_128.gif]  

Explore Solution 3.3.

[Graphics:../Images/AnalyticFunctionMod_gr_129.gif]





 

 

 

Aside.  This can be compared with expanding F[z] and calculating the derivative

[Graphics:../Images/AnalyticFunctionMod_gr_131.gif]




[Graphics:../Images/AnalyticFunctionMod_gr_132.gif]

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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