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math.CA2023
A study on the bilinear equation of the sixth Painlevé transcendents
Tatsuya Hosoi, Hidetaka Sakai
The sixth Painlevé equation is a basic equation among the non-linear differential equations with three fixed singularities, corresponding to Gauss's hypergeometric differential equ…
math.CA2014
Spectral types of linear -difference equations and -analog of middle convolution
Hidetaka Sakai, Masashi Yamaguchi
We give a -analog of middle convolution for linear -difference equations with rational coefficients. In the differential case, middle convolution is defined by Katz, and he e…
math.CA2012★ 28 cited
Degeneration scheme of 4-dimensional Painlevé-type equations
Hiroshi Kawakami, Akane Nakamura, Hidetaka Sakai
Four 4-dimensional Painlevé-type equations are obtained by isomonodromic deformation of Fuchsian equations: they are the Garnier system in two variables, the Fuji-Suzuki system, th…