Exercise 9.  Use residues to find   .  

9 (a).  .  

Solution 9 (a).

See text and/or instructor's solution manual.

Answer.   .  

Aside.   We could use Table 9.1 of z-transforms and get the solution  

                      

Solution.   Using residues we get

                      

Therefore,

                    .  

We are done.   

Aside.  We can let Mathematica double check our work.

Aside.  We can use Mathematica's  Limit  and  Residue  subroutines.

          The Maple code using limits is similar  

  

                                                            


          The Maple code using residues is similar  

  

                                                            


          We can use Maple's subroutine to find the inverse.  

  

                                                            

We are really done.   

Aside.  We can graph some of the terms in the sequence.

                                                                                                                        The sequence   .  

This solution is complements of the authors.

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