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arXiv · 1808.03014

Extensions of the Classical Transformations of 3F2

Robert S. Maier
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Abstract

It is shown that the classical quadratic and cubic transformation identities satisfied by the hypergeometric function ${}_3F_2$ 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 ${}_7F_6(1)$ series and balanced ${}_4F_3(1)$ series, and extensions of other summation identities.

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Robert S. Maier. 2018-08-09. Extensions of the Classical Transformations of 3F2. https://doi.org/10.1016/j.aam.2019.01.002

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