Painleve sigma-equations S1, S2, S4 and their value distribution

Abstract

Local solutions of Painleve equations P1, P2, P4, as well as of the equations  S1, S2, S4 satisfied by their Hamiltonians, can be extended to functions meromorphic in C. This way they become a point of interest for value distribution theory. Distribution of values of solutions of P1, P2 and P4
is already well described. In the paper we discuss mostly S1, S2 and S4 in this context. In particular, we pay attention to deficient, asymptotic and ramified values of solutions of these equations.