Hypergeometric $τ$ Functions of the $q$-Painlevé Systems of Types $A_4^{(1)}$ and $(A_1+A_1')^{(1)}$

Nobutaka Nakazono

doi:10.3842/SIGMA.2016.051

paper

Hypergeometric $τ$ Functions of the $q$ -Painlevé Systems of Types $A_{4}^{(1)}$ and $(A_{1} + A_{1}^{'})^{(1)}$

arXiv:1601.05327 · doi:10.3842/SIGMA.2016.051

Abstract

We consider $q$ -Painlevé equations arising from birational representations of the extended affine Weyl groups of $A_{4}^{(1)}$ - and $(A_{1} + A_{1})^{(1)}$ -types. We study their hypergeometric solutions on the level of $τ$ functions.

References in corpus (5)

Hypergeometric solutions to the q-Painlevé equation of type $A_{4}^{(1)}$
Hypergeometric $τ$ -Functions of the $q$ -Painlevé System of Type $E_{7}^{(1)}$
Lattice equations arising from discrete Painlevé systems (I): $(A_{2} + A_{1})^{(1)}$ and $(A_{1} + A_{1}^{'})^{(1)}$ cases
Lax pairs of discrete Painlevé equations: $(A_{2} + A_{1})^{(1)}$ case
Hypergeometric $τ$ Function of the $q$ -Painlevé Systems of Type $(A_{2} + A_{1})^{(1)}$

Hypergeometric τ Functions of the q-Painlevé Systems of Types A4(1)​ and (A1​+A1′​)(1)

Abstract

References in corpus (5)

Hypergeometric $τ$ Functions of the $q$ -Painlevé Systems of Types $A_{4}^{(1)}$ and $(A_{1} + A_{1}^{'})^{(1)}$