Exercise 1.  Find      for the following functions:

1 (g).   .

Solution 1 (g).

See text and/or instructor's solution manual.

Answer.   

Solution.   Use the fact that    and express this function in the following form

                      

The function    has a removable singularity at .  

Here we have    and according to Definition 8.1  

the residue is seen to be  .  

We are done.   

Aside.  We can let Mathematica double check our work.

Maple can check our work too!

     > series( sin(z)/z, z=0,12 );

               

We are really really done.   

Aside.  Both and are capable of finding residues.

     > residue( sin(z)/z, z=0 );

               0

This solution is complements of the authors.

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