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

抄録

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.