English

Hypergeometric $\tau$-Functions of the $q$-Painlev\'e System of Type $E_7^{(1)}$

Exactly Solvable and Integrable Systems 2009-03-25 v1 Classical Analysis and ODEs

Abstract

We present the τ\tau-functions for the hypergeometric solutions to the qq-Painlev\'e system of type E7(1)E_7^{(1)} in a determinant formula whose entries are given by the basic hypergeometric function 8W7{}_8W_7. By using the W(D5)W(D_5) symmetry of the function 8W7{}_8W_7, we construct a set of twelve solutions and describe the action of W~(D6(1))\widetilde{W}(D_6^{(1)}) on the set.

Keywords

Cite

@article{arxiv.0903.4102,
  title  = {Hypergeometric $\tau$-Functions of the $q$-Painlev\'e System of Type $E_7^{(1)}$},
  author = {Tetsu Masuda},
  journal= {arXiv preprint arXiv:0903.4102},
  year   = {2009}
}