On the algebraic solutions of the Painlevé-III (D7) equation

The D7 degeneration of the Painlevé-III equation has solutions that are rational functions of x1/3 for certain parameter values. We apply the isomonodromy method to obtain a Riemann-Hilbert representation of these solutions. We demonstrate the utility of this representation by analyzing rigorously the behavior of the solutions in the large parameter limit. •The algebraic solutions of the degenerate D7 type Painlevé-III equation are studied.•A Riemann-Hilbert representation of these solutions is deduced by the isomonodromy method.•That representation is used to study the solutions in the large-parameter limit.