Extensions of the Classical Transformations of 3F2
arXiv:1808.03014 · doi:10.1016/j.aam.2019.01.002
Abstract
It is shown that the classical quadratic and cubic transformation identities satisfied by the hypergeometric function 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 series and balanced series, and extensions of other summation identities.
22 pages, expanded version, to appear in Advances in Applied Mathematics