The Padé interpolation method applied to additive difference Painlevé equations

Abstract

We study Padé interpolation problems on an additive grid, related to additive difference (d-) Painlevé equations of type $$E_7^{(1)}$$ , $$E_6^{(1)}$$ , $$D_4^{(1)}$$ and $$A_3^{(1)}$$ . By choosing suitable Padé problems, we can derive time evolution equations, scalar Lax pairs of contiguous type and determinant formulae of special solutions given in terms of hypergeometric functions, for the corresponding d-Painlevé equations.