Solutions to a q-Analog of the Painlevé III Equation of Type D7(1)

Nobutaka Nakazono; Seiji Nishioka

doi:10.1619/fesi.56.415

Funkcialaj Ekvacioj

Print ISSN : 0532-8721

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Volume 56 (2013) Issue 3
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Solutions to a q-Analog of the Painlevé III Equation of Type D₇⁽¹⁾

Nobutaka Nakazono, Seiji Nishioka

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Keywords: q-Painlevé equation, q-difference equation, Algebraic function solution, τ function, Irreducibility

JOURNAL FREE ACCESS

2013 Volume 56 Issue 3 Pages 415-439

DOI https://doi.org/10.1619/fesi.56.415

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Abstract

This paper treats a q-analog of the Painlevé III equation of type D₇⁽¹⁾. We study its algebraic function solutions and transcendental function solutions. We construct algebraic function solutions expressed in terms of Laurent polynomials and prove the irreducibility of the equation in the sense of decomposable extensions.

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