An elliptic hypergeometric integral with W(F4) symmetry

In this article we give a new transformation between elliptic hypergeometric beta integrals, which gives rise to a Weyl group symmetry of type F ₄. The transformation is a generalization of a series transformation discovered by Langer, Schlosser, and Warnaar (SIGMA 5:055, 2009). Moreover we consider various limits of this transformation to basic hypergeometric functions obtained by letting p tend to 0.