Bilinear structure and Schlesinger transforms of the $q$-P${}_{\mathrm{III}}$ and $q$-P${}_{\mathrm{VI}}$ equations

M. Jimbo, H. Sakai, A. Ramani +1

We show that the recently derived ($q$-) discrete form of the Painlevé VI equation can be related to the discrete P${}_{\mathrm{III}}$, in particular if one uses the full freedom in the i…