On the Schlesinger transformations of the sixth Painlevé equation

Abstract

Following the recent discovery of two new Schlesinger transformations (ST) for the sixth Painlevé equation, we give the interrelations between all the known STs. We thus isolate the unique one which at the same time conserves the independent variable and is not a product of other STs.

in French, LaTeX, 5 pages, to appear, Comptes rendus Acad. Sci. Paris

Cited by in corpus (4)

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• New contiguity relation of the sixth Painlevé equation from a truncation
• Geometry of the Ising persistence problem and the universal Bonnet-Manin Painlevé VI distribution
• A truncation for obtaining all the first degree birational transformations of the Painlevé transcendents