The Picard solution of the sixth Painlev'e equation and asymptotic forms found by Power Geometry. Preprint of the Keldysh Institute of Applied
Abstract:
The sixth Painlev'e equation has solutions, which in the generic case determined new transcendent functions [1] (Painlev'e transcendents). Only for some values of complex parameters of the equation it is possible to write its solution, which is expressed in elementary or known special functions. One of the most famous solution of the sixth Painlev'e equation is the Picard solution. By the methods of Power Geometry we found all asymptotic expansions of solutions to the sixth Painlev'e equation for all values its complex parameters of the five types. The purpose of this work is: to compare the known solution with asymptotic forms, found by Power Geometry.
Publication language:russian, pages:8
Research direction:
Mathematical problems and theory of numerical methods
