Certain transformations for hypergeometric series in the p-adic setting

DOI10.1142/S1793042115500359zbMATH Open1365.11121arXiv1403.3607OpenAlexW2963826238MaRDI QIDQ5248151

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Publication date: 27 April 2015

Published in: (Search for Journal in Brave)

Abstract: 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.

Full work available at URL: https://arxiv.org/abs/1403.3607

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