what is the nature of singularity of the function f(x)=exp(-1/z) where z is a complex number? now i arrive at two different results by progressing in two different ways. 1) if we expand the series f(z)=1-1/z+1/2!(z^2)-... then i can say that z=0 is an essential singularity. 2) now again if i take the limit of the function from either sides of zero, i see it exists finitely, therefore not a singular point at all.