Zobrazeno 1 - 10
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pro vyhledávání: '"Takemura, Kouichi"'
Autor:
Takemura, Kouichi
We find kernel functions of the $q$-Heun equation and its variants. We apply them to obtain $q$-integral transformations of solutions to the $q$-Heun equation and its variants. We discuss special solutions of the $q$-Heun equation from the perspectiv
Externí odkaz:
http://arxiv.org/abs/2309.09341
Autor:
Arai, Yumi, Takemura, Kouichi
Publikováno v:
SIGMA 19 (2023), 037, 40 pages
The $q$-middle convolution was introduced by Sakai and Yamaguchi. In this paper, we reformulate $q$-integral transformations associated with the $q$-middle convolution. In particular, we discuss convergence of the $q$-integral transformations. As an
Externí odkaz:
http://arxiv.org/abs/2209.02227
Autor:
Takemura, Kouichi
We investigate the symmetry of the linear q-difference equations which are associated with some q-Painlev\'e equations. We apply it for adjustment of the expression of the time evolution on the q-Painlev\'e equations in terms of the Weyl group symmet
Externí odkaz:
http://arxiv.org/abs/2201.07529
Publikováno v:
SIGMA 18 (2022), 056, 21 pages
A $q$-deformation of the middle convolution was introduced by Sakai and Yamaguchi. We apply it to a linear $q$-difference equation associated with the $q$-Painlev\'e VI equation. Then we obtain integral transformations. We investigate the $q$-middle
Externí odkaz:
http://arxiv.org/abs/2201.03960
We show that the q-Heun equation and its variants appear in the linear q-difference equations associated to some q-Painlev\'e equations by considering the blow-up associated to their initial-value spaces. We obtain the firstly degenerated Ruijsenaars
Externí odkaz:
http://arxiv.org/abs/2110.13860
Variants of the q-hypergeometric equation were introduced in our previous paper with Hatano. In this paper, we consider degenerations of the variant of the q-hypergeometric equation, which is a q-analogue of confluence of singularities in the setting
Externí odkaz:
http://arxiv.org/abs/2005.13223
We introduce two variants of $q$-hypergeometric equation. We obtain several explicit solutions of variants of $q$-hypergeometric equation. We show that a variant of $q$-hypergeometric equation can be obtained by a restriction of $q$-Appell equation o
Externí odkaz:
http://arxiv.org/abs/1910.12560
Autor:
Takemura, Kouichi
The $q$-Heun equation is a $q$-difference analogue of Heun's differential equation. We review several solutions of Heun's differential equation and investigate polynomial-type solutions of $q$-Heun equation. The limit $q\to 1$ corresponding to Heun's
Externí odkaz:
http://arxiv.org/abs/1903.02415
It is known that the q-Heun equation has polynomial-type solutions in some special cases, and the condition for the accessory parameter E is described by the roots of the spectral polynomial. We investigate the spectral polynomial by considering the
Externí odkaz:
http://arxiv.org/abs/1811.11677
Publikováno v:
Journal of Difference Equations and Applications 25 (2019) 647-664
We study polynomial-type solutions of the $q$-Heun equation, which is related with quasi-exact solvability. The condition that the $q$-Heun equation has a non-zero polynomial-type solution is described by the roots of the spectral polynomial, whose v
Externí odkaz:
http://arxiv.org/abs/1809.01428