pole
isolated singularity of a holomorphic function 𝑓 such that 1/𝑓 has a zero and is holomorphic at the singularity
simple pole
pole of order 1
removable singularity
pole of order zero; a point at which a holomorphic function is undefined, but it is possible to redefine the function at that point in such a way that the resulting function is regular in a neighbourhood of that point