Computation of RS-pullback transformations for algebraic Painleve VI solutions

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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

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Classical Analysis and ODEs, 34M55, 33E17, 57M12

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http://salesiana.dossiersoluciones.com/handle/123456789/171400

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/0705.2963
 http://arxiv.org/abs/0705.2963

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arXiv