The Malgrange–Galois groupoid of the Painlevé VI equation with parameters

Abstract The Malgrange–Galois groupoid of Painlevé IV equations is known to be, for very general values parameters, the pseudogroup transformations phase space preserving a volume form, time form and equation. Here we compute VI family including all parameters as new dependent variables. We conclude that it parameter values, differential independent variable, in variables This implies solution equation depending analytically on does not satisfy any partial (including derivatives with respect parameters) which derived from VI.