Exercise 1.  Establish that    for all z.  

Solution 1.

See text and/or instructor's solution manual.

Solution.  

                      

Now change the index in the summation    from k to n using    and  and get

                    .

Therefore,  

                    .  

We are done.   

Aside.  We can let Mathematica double check our work.

This solution is complements of the authors.

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