Geodesic
On $q$-Deformations of the Heun Equation
Symmetry, integrability and geometry: methods and applications, Tome 14 (2018) Cet article a éte moissonné depuis la source Math-Net.Ru

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The $q$-Heun equation and its variants arise as degenerations of Ruijsenaars–van Diejen operators with one particle. We investigate local properties of these equations. In particular we characterize the variants of the $q$-Heun equation by using analysis of regular singularities. We also consider the quasi-exact solvability of the $q$-Heun equation and its variants. Namely we investigate finite-dimensional subspaces which are invariant under the action of the $q$-Heun operator or variants of the $q$-Heun operator.
Keywords: Heun equation; $q$-deformation; regular singularity; quasi-exact solvability; degeneration. 
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     author = {Kouichi Takemura},
     title = {On $q${-Deformations} of the {Heun} {Equation}},
     journal = {Symmetry, integrability and geometry: methods and applications},
     year = {2018},
     volume = {14},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SIGMA_2018_14_a60/}
}
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Kouichi Takemura. On $q$-Deformations of the Heun Equation. Symmetry, integrability and geometry: methods and applications, Tome 14 (2018). http://geodesic.mathdoc.fr/item/SIGMA_2018_14_a60/

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