5 papers · 1 filter
Reducibility of symmetry on -Painlevé equations
Chihiro Sato, Kouichi Takemura, Ohka Yamashita
It is known that -Painlevé equations admit the symmetry of the extended affine Weyl groups. Kajiwara, Noumi and Yamada developed a unified description of the symmetry by introdu…
Degenerations of -Heun equation
Chihiro Sato, Kouichi Takemura
We obtain several degenerations of the -Heun equation by considering the linear -difference equations associated to several -Painlevé equations. We establish definitions o…
Reformulation of -Middle Convolution and Applications
Yumi Arai, Kouichi Takemura
We reformulate the -convolution and the -middle convolution introduced by Sakai and Yamaguchi, and we introduce -analogues of the addition which is related to the gauge-tr…
On zeros of polynomials associated with Heun class equations
Mizuki Mori, Kouichi Takemura
Schäfke and Schmidt established that the asymptotics of the coefficients of the local solution to some linear differential equation is related to global structures of solutions. Th…
Kernel Function, -Integral Transformation and -Heun Equations
Kouichi Takemura
We find kernel functions of the -Heun equation and its variants. We apply them to obtain -integral transformations of solutions to the -Heun equation and its variants. We…