Geodesic
Hypergeometric Solutions of the $A_4^{(1)}$-Surface $q$-Painlevé IV Equation
Symmetry, integrability and geometry: methods and applications, Tome 10 (2014) Cet article a éte moissonné depuis la source Math-Net.Ru

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We consider a $q$-Painlevé IV equation which is the $A_4^{(1)}$-surface type in the Sakai's classification. We find three distinct types of classical solutions with determinantal structures whose elements are basic hypergeometric functions. Two of them are expressed by ${}_2\varphi_1$ basic hypergeometric series and the other is given by ${}_2\psi_2$ bilateral basic hypergeometric series.
Keywords: $q$-Painlevé equation; basic hypergeometric function; affine Weyl group; $\tau$-function; projective reduction; orthogonal polynomial. 
@article{SIGMA_2014_10_a89,
     author = {Nobutaka Nakazono},
     title = {Hypergeometric {Solutions} of the $A_4^{(1)}${-Surface} $q${-Painlev\'e} {IV} {Equation}},
     journal = {Symmetry, integrability and geometry: methods and applications},
     year = {2014},
     volume = {10},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SIGMA_2014_10_a89/}
}
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Nobutaka Nakazono. Hypergeometric Solutions of the $A_4^{(1)}$-Surface $q$-Painlevé IV Equation. Symmetry, integrability and geometry: methods and applications, Tome 10 (2014). http://geodesic.mathdoc.fr/item/SIGMA_2014_10_a89/

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