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Hypergeometric special solutions for $d$-Painlev\'e equations. (arXiv:1706.10101v1 [nlin.SI] CROSS LISTED)

来源于:arXiv
We have studied 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 solving those problems, we can derive time evolution equations, Lax pairs of scalar type and determinant formulae of special solutions, for the corresponding $d$-Painlev\'e equations. We show how the special solutions are expressed as determinant formulae by using terminating (generalized) hypergeometric functions. 查看全文>>