10/17/2009, 04:37 PM

(10/17/2009, 10:47 AM)andydude Wrote: It is well known that there is a logarithmic singularity at -2, which is a specific kind of essential singularity.

A logarithmic singularity is not an essential singularity!

All 3 types: removable singularity, pole and essential singularity, are isolated singularities, i.e. the function is holomorphic in vicinity except at that singularity.

This is not the case for the logarithm at 0.

0 is a branchpoint of the logarithm and of roots.

Quote:It is also known that there are essential singularities at -3, -4, etc, but exactly what kind of singularities these are is not well known.

Jay would call them doubly, trice, etc logarithmic. These all are branchpoints not isolated singularities.