Certain Transformations for Hypergeometric series in p-adic setting
classification
🧮 math.NT
keywords
functionadicfieldsfinitehypergeometriccdotscertainfunctions
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In \cite{mccarthy2}, McCarthy defined a function $_{n}G_{n}[\cdots]$ using the Teichm\"{u}ller character of finite fields and quotients of the $p$-adic gamma function. This function extends hypergeometric functions over finite fields to the $p$-adic setting. In this paper, we give certain transformation formulas for the function $_{n}G_{n}[\cdots]$ which are not implied from the analogous hypergeometric functions over finite fields.
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