Hypergeometric Solutions of the $A_4^{(1)}$-Surface $q$-Painlev\'e IV Equation

Nobutaka Nakazono

doi:10.3842/sigma.2014.090

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arXiv · 1301.2401

Hypergeometric Solutions of the $A_4^{(1)}$-Surface $q$-Painlev\'e IV Equation

Nobutaka Nakazono

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Abstract

We consider a $q$-Painlev\'e 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.

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Nobutaka Nakazono. 2013-01-11. Hypergeometric Solutions of the $A_4^{(1)}$-Surface $q$-Painlev\'e IV Equation. https://doi.org/10.3842/sigma.2014.090

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