Extensions of the Classical Transformations of 3F2. (arXiv:1808.03014v1 [math.CA])

It is shown that the classical quadratic and cubic transformations of the generalized hypergeometric function ${}_3F_2$ have extensions involving hypergeometric functions of higher order, the additional parameter pairs of which have integral differences. The added parameters are nonlinearly constrained: they are the negated roots of certain dual Hahn and Racah polynomials. Applications of the new function transformations include the extending of Whipple's formula relating very well poised ${}_7F_6(1)$ series and balanced ${}_4F_3(1)$ series, to versions that have additional, nonlinearly constrained parameters. 查看全文>>