Question

8. (30) This problem has several parts spread over several pages. Note that you can use the conclusion of a previous part even if you were unable to work that part Assume throughout that f in analytic and non-zero in BR(z0) for some R> 0 so that f has an isolated singularity at o (d) Show that if f has an isolated singularity at z0 and g(z) exp(f(z)), then g has a removable singularity at zo if and only if f has a removable singularity at zo

Answer 1

Knoo that Rie manns Remova ble singularit Tem that, f has a emovab le singularity z. s bounded in some deleted at neighbo hood upposeaz has emovable singularity at z a(z) is blu nded in some deleted neighbouγhod exp(f(z)) İs bdd in some deleted nbd But exp (ta) is bounded when fa)ir bdd s bdd in some deleted nbd af z. - converse ly >f2 s bdld n some deleted nb f z has a emovable singularity atz