Abstract
We prove two general formulas for a two-parameter family of hypergeometric $\3F2(z)$ functions over a finite field $\F_q$, where $q$ is a power of an odd prime. Each formula evaluates a $\3F2$ in terms of a $\2F1$ over $\F_{q^2}$. As applications, we evaluate infinite one-parameter families of $\3F2(\frac{1}{4})$ and $\3F2(-1)$, thereby extending results of J. Greene--D. Stanton and K. Ono, who gave evaluations in special cases.
Citation
Ron Evans. John Greene. "Evaluations of hypergeometric functions over finite fields." Hiroshima Math. J. 39 (2) 217 - 235, July 2009. https://doi.org/10.32917/hmj/1249046338
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