Movable algebraic singularities of second-order ordinary differential equations

G. Filipuk, R. G. Halburd

Any nonlinear equation of the form y''=\sum_{n=0}^N a_n(z)y^n has a (generally branched) solution with leading order behaviour proportional to (z-z_0)^{-2/(N-1)} about a point z_0,…