Construction of Hypergeometric Solutions to the q-Painlevé Equations
نویسنده
چکیده
The list of q-Painlevé equations we are going to investigate is given in section 3 below. We remark that these q-Painlevé equations were discovered through various approaches to discrete Painlevé equations, including singularity confinement analysis, compatibility conditions of linear difference equations, affine Weyl group symmetries and τ-functions on the lattices. Also, in Sakai’s framework [2], each of these q-Painlevé equations is constructed in a unified manner as the birational action of a translation of the corresponding affine Weyl group on a certain family of rational surfaces. In [4] we have introduced the formulation of discrete Painlevé equations based on the geometry of plane curves on P2. On that basis we were able in the first part of [1] to find suitable coordinates for linearization of the q-Painlevé equations into three-term relations of hypergeometric functions. As a result we obtained the following degeneration diagram of basic hypergeometric functions corresponding to (1):
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Hypergeometric solutions to the q-Painlevé equations
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