Solution 17.

Solution.   Since   [Graphics:../Images/LaurentSeriesModHome_gr_690.gif]  the Laurent series   [Graphics:../Images/LaurentSeriesModHome_gr_691.gif]    is valid for  [Graphics:../Images/LaurentSeriesModHome_gr_692.gif].  

Letting  [Graphics:../Images/LaurentSeriesModHome_gr_693.gif]  gives   [Graphics:../Images/LaurentSeriesModHome_gr_694.gif]   immediately.

Since   [Graphics:../Images/LaurentSeriesModHome_gr_695.gif]  by Laurent's Theorem,   

                    [Graphics:../Images/LaurentSeriesModHome_gr_696.gif],    for all integers  n.

Parametrizing  [Graphics:../Images/LaurentSeriesModHome_gr_697.gif]  with  [Graphics:../Images/LaurentSeriesModHome_gr_698.gif]  for  [Graphics:../Images/LaurentSeriesModHome_gr_699.gif]  gives

                      [Graphics:../Images/LaurentSeriesModHome_gr_700.gif]    

 

 

  

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

This solution is complements of the authors.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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