Algebraic branch point
= Algebraic branch point
{title2=$w(z)=\sum_{j=j_0}^{\infty}c_j(z-a)^{j/k}$}
At an algebraic <branch point>, a local solution becomes <meromorphic> after the finite substitution $z-a=t^k$. The displayed convergent expansion has only finitely many negative terms. A square-root <branch point> corresponds to $k=2$; an <essential singularity> or <logarithmic singularity> need not become meromorphic under any such finite substitution.