UMD Analysis Qualifying Exam/Jan07 Complex

Problem 2 edit

Compute the partial fractions decomposition of  .

Solution 2 edit

Problem 4 edit

Consider the series  

(a) Find the domain   where the series is convergent

(b) Prove that for any  , for some polynomial  .

(c) Prove that if   has analytic extension from   then it has analytic extension to  .

(d) Prove that   has no analytic extension from  .

Solution 4 edit

Problem 6 edit

Solution 6 edit