Solution 5.

See text and/or instructor's solution manual.

Solution.   By Theorem 7.11,   ,   where   is analytic at .  

Then  

                      

where  .  

Since    are analytic, so is the linear combination  .   

Also, it is easy to see that  

                    .  

Now apply Theorem 7.11 and conclude that    has a zero of order    at  .  

This solution is complements of the authors.

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