I'm reading text about generating functions and how to reveal their asymptotic behaviour by means of analysing their singularities. In this context the term "algebraic singularity" or in German "algebraische Singularität" is used. An example is given: $p(x)=\frac{1-\sqrt{1-4x}}{2}$.
It's clear to me what a singularity is, but I can't find what they mean with algebaic in this context.
Edit: Is this term used as synonym for essential singularities, i.e. singularities not being poles?