For the hypergeometric function of unit argument F-3(2)(1) we prove the existence and uniqueness of three-term contiguous relations with arbitrary integer shifts. We show that not only the original 3F2(1) function but also other five functions related to it satisfy one and the same three-term relation. This fact together with the uniqueness mentioned above provides three-term relations with a group symmetry of order 72. (C) 2018 Elsevier Inc. All rights reserved.
