Solution 19 (b).

See text and/or instructor's solution manual.

Solution.   The point    is a removable singularity,  since    may be redefined at    to be analytic.

Obviously, this redefinition should be  .

Hence,    is not continuous at .

Therefore,    is not analytic at .

The minimum distance the singularity to the center    is

                    .

So that Corollary 7.3 only guarantees that the Taylor series  

                      

converges to on all of  .    

This solution is complements of the authors.

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