Solution 16.

See text and/or instructor's solution manual.

                    The point    that lies inside the contour  .  

Solution.  Applying Cauchy's Integral formula for derivatives      with      we write   

                    

When   use the formula  .

Then multiplication by    produces the desired result  

                    .  

When   use the formula  .  

Then multiplication by    produces the desired result  

                    .  

When   use the formula  .  

Then multiplication by    produces the desired result  

                    .  

When   use the formula  .  

Then multiplication by    produces the desired result  

                    .  

When   use the formula  .

Then multiplication by    produces the desired result  

                    .  

This solution is complements of the authors.

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