On two Thomae-type transformations for hypergeometric series with integral parameter differences

Abstract

We obtain two new Thomae-type transformations for hypergeometric series with $r$ pairs of numeratorial and denominatorial parameters differing by positive integers. This is achieved by application of the so-called Beta integral method developed by Krattenthaler and Rao [Symposium on Symmetries in Science (ed. B. Gruber), Kluwer (2004)] to two recently obtained Euler-type transformations. Some special cases are given.