CSIR NET Mathematics 2022| Complex Analysis (3 NOVEMBER)

The Loci of the point z satisfying is

Consider the function f(z) =  for 0 < |z| < 1 where m n are positive integers. Then z _ Q Is

find the residue of at its essential singularity

For a positive integer p, consider the holomorphic function for z ∈ . For which values of p does there exist a holomorphic function such that f(z)=g’(z) for z ∈ ?

Let f(z)=cos.then for f(z),z= 0 is