On some properties of auxiliary functions associated to the Painleve equations $P_{II} - P_{V}$

Painleve equations are nonlinear second order ordinary differential equations, solutions of which have no movable critical points (i.e., solutions are meromorphic on the universal cover of P1-{several fixed singularities}). Painleve transcendents are regarded as nonlinear special functions due to numerous applications in pure and applied mathematics. I shall speak about certain auxiliary functions associated to the  Painleve equations $P_{II}- P_{V}$ and discuss some of their properties.