Solution 15 (c).

Solution.   Combining the results of parts (a) and (b) we have

                    [Graphics:../Images/LaurentSeriesModHome_gr_648.gif]  


Therefore,    [Graphics:../Images/LaurentSeriesModHome_gr_649.gif].  

We are done.   

Aside.  We can let Mathematica double check our work.

[Graphics:../Images/LaurentSeriesModHome_gr_650.gif]

[Graphics:../Images/LaurentSeriesModHome_gr_651.gif]

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 



This solution is complements of the authors.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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