Computation of RS-pullback transformations for algebraic Painleve VI solutions

Abstract

Algebraic solutions of the sixth Painleve equation can be computed using pullback transformations of hypergeometric equations with respect to specially ramified rational coverings. In particular, as was noticed by the second author and Doran, some algebraic solutions can be constructed from a rational covering alone, without computation of the pullbacked Fuchsian equation. But the same covering can be used to pullback different hypergeometric equations, resulting in different algebraic Painleve VI solutions. This paper presents computations of explicit RS-pullback transformations, and derivation of algebraic Painleve VI solutions from them.

18 pages; 7 figures; Schlesinger transformations (and some examples) are brought to the new paper http://arxiv.org/abs/0705.2963

References in corpus (7)

• Transformations ${RS}_4^2(3)$ of the Ranks $\le 4$ and Algebraic Solutions of the Sixth Painlevé Equation
• Transformations of some Gauss hypergeometric functions
• Some explicit solutions to the Riemann-Hilbert problem
• Computation of highly ramified coverings
• Special Functions of the Isomonodromy Type, Rational Transformations of Spectral Parameter, and Algebraic Solutions of the Sixth Painlevé Equation
• Remarks Towards the Classification of $R{S}_4^2(3)$-Transformations and Algebraic Solutions of the Sixth Painlevé Equation
• Schlesinger transformations for algebraic Painleve VI solutions

Cited by in corpus (1)

• Computation of highly ramified coverings