Solution 19.

See text and/or instructor's solution manual.

Solution.  Let  [Graphics:../Images/IntegralRepresentationModHome_gr_959.gif],  which is analytic everywhere.  

By Cauchy's integral formulas,  [Graphics:../Images/IntegralRepresentationModHome_gr_960.gif]  and we can write

                    [Graphics:../Images/IntegralRepresentationModHome_gr_961.gif],  

                    [Graphics:../Images/IntegralRepresentationModHome_gr_962.gif],  

                    [Graphics:../Images/IntegralRepresentationModHome_gr_963.gif],

                    [Graphics:../Images/IntegralRepresentationModHome_gr_964.gif]

By definition we have  

                    [Graphics:../Images/IntegralRepresentationModHome_gr_965.gif],

Therefore  [Graphics:../Images/IntegralRepresentationModHome_gr_966.gif].  

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

This solution is complements of the authors.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

(c) 2008 John H. Mathews, Russell W. Howell