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Preprint Number 503
503. Joel Nagloo and Anand Pillay
On the algebraic independence of generic Painlevé transcendents
Submission date: 7 September 2012.
We prove that if y = f(y,y',t) is a generic Painlevé equation from among the classes II to V then any collection of distinct solutions and their derivatives are algebraically independent over C(t). (Already proved by Nishioka for the single Painlevé I equation). For generic Painlevé VI we prove a slightly weaker statement.
Mathematics Subject Classification: 14H05, 14H70, 34M55, 03C60
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