UMD Analysis Qualifying Exam/Jan07 Complex

Problem 2Edit

Compute the partial fractions decomposition of  .

Solution 2Edit

Problem 4Edit

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 4Edit

Problem 6Edit

Solution 6Edit