Teaching CSIR NET Mock Test Series Mathematical Science Complex Analysis Theorems of Complex analysis
Consider the function
\(f\left( z \right) = \frac{{{{\left( {\sin z} \right)}^m}}}{{{{\left( {1 - \cos z} \right)}^n}}}for\,0 < \left| z \right| < 1\)
where m, n are positive integers. Then z = 0 is
1
A removable singularity if m ≥ 2n
2
A pole if m < 2n
3
A pole if m ≥ 2n
4
An essential singularity for some values of m, n