We present a systematization of the special-function type solutions of continuous and discrete Painlevé equations. Our method is to start from PVI and construct its special solutions from the solutions of the hypergeometric equation, and by coalescence obtain the lower Painlevé equations together with their special solutions. In the discrete case we study the 'symmetric', one-component, three-point mapping forms of discrete Painlevé equations starting from d-PV.
All Science Journal Classification (ASJC) codes
- Statistical and Nonlinear Physics
- Mathematical Physics
- Physics and Astronomy(all)