High Quality Content by WIKIPEDIA articles! In mathematics, Painleve transcendents are solutions to certain nonlinear second-order ordinary differential equations in the complex plane with the Painleve property (the only movable singularities are poles), but which are not generally solvable in terms of elementary functions. They are named for the French mathematician (and prime minister) Paul Painleve who found them around 1900.Painleve transcendents have their origin in the study of special functions, which often arise as solutions of differential equations, as well as in the study of isomonodromic deformations of linear differential equations. One of the most useful classes of special functions are the elliptic functions.

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