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This article is cited in 1 scientific paper (total in 1 paper)
Hypergeometric Solutions of the $A_4^{(1)}$-Surface $q$-Painlevé IV Equation
Nobutaka Nakazono School of Mathematics and Statistics, The University of Sydney, New South Wales 2006, Australia
Abstract:
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.
Received: June 6, 2013; in final form August 14, 2014; Published online August 22, 2014
Citation:
Nobutaka Nakazono, “Hypergeometric Solutions of the $A_4^{(1)}$-Surface $q$-Painlevé IV Equation”, SIGMA, 10 (2014), 090, 23 pp.
Linking options:
https://www.mathnet.ru/eng/sigma955 https://www.mathnet.ru/eng/sigma/v10/p90
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Abstract page: | 135 | Full-text PDF : | 37 | References: | 46 |
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