The Pad\'e interpolation method applied to additive difference Painlev\'e equations
The Pad\'e interpolation method applied to additive difference Painlev\'e equations
We study Pad\'e interpolation problems on an additive grid, related to additive difference ($d$-) Painlev\'e equations of type $E_7^{(1)}$, $E_6^{(1)}$, $D_4^{(1)}$ and $A_3^{(1)}$. By choosing suitable Pad\'e 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 $d$-Painlev\'e equations.
Comment: 25 pages, 4figures, 5tables
Nonlinear Sciences - Exactly Solvable and Integrable Systems, Mathematics - Classical Analysis and ODEs, 33D15, 34M55, 39A10, 41A05, 41A21, Mathematical Physics
Nonlinear Sciences - Exactly Solvable and Integrable Systems, Mathematics - Classical Analysis and ODEs, 33D15, 34M55, 39A10, 41A05, 41A21, Mathematical Physics
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