Extensions of the classical transformations of the hypergeometric function 3F2

It is shown that the classical quadratic and cubic transformation identities satisfied by the hypergeometric function F-3(2) can be extended to include additional parameter pairs, which differ by integers. In the extended identities, which involve hypergeometric functions of arbitrarily high order, the added parameters are nonlinearly constrained: in the quadratic case, they are the negated roots of certain orthogonal polynomials of a discrete argument (dual Hahn and Racah ones). Specializations and applications of the extended identities are given, including an extension of Whipple's identity relating very well poised F-7(6) (1) series and balanced F-4(3) (1) series, and extensions of other summation identities. (C) 2019 Elsevier Inc. All rights reserved.