New Coalescences for the Painlev\'e Equations

Abstract

The Painlev\'e equations are here connected to other classes of equations with the Painlev\'e Property (Ince's equations) by the same degeneracy procedure that connects the Painlev\'e equations (coalescence). These Ince's equations here are also connected among themselves like in the traditional Painlev\'e's coalescence cascade. Such degeneracy is considered also for the special equations, symmetric equations and B\"acklund transformations.