Power Expansions of Solutions to the Sixth Painleve’ Equation.
Abstract:
By means of Power Geometry, shortly described in §1, in the generic case we compute all power expansions of solutions to the sixth Painleve' equation at points x = 0, x = ∞ (§2) and x = 1 (§3). Three symmetries of the equation allow reducing all these expansions to three basic families. One of them begins by the term with arbitrary power exponent that means a new type of singularity of the equation.
Publication language:russian, pages:24
Research direction:
Mathematical problems and theory of numerical methods
