Strange Evaluations of Hypergeometric Series
Ira M. Gessel, Dennis Stanton · SIAM Journal on Mathematical Analysis · 1982
Many evaluations of terminating hypergeometric series at arguments other than 1 are given. Some are equivalent to some unpublished work of Gosper, while others are new. In particular, two new evaluations of ${}_7 F_6 $’s with four parameters are stated. The main technique is a change of variables formula which is equivalent to the Lagrange inversion formula. A new proof of Whipple’s transformation of a very well poised ${}_7 F_6 $ into a Saalschützian ${}_4 F_3 $ is a corollary.