Certain transformations and values of p-adic hypergeometric functions

Sulakashna; Rupam Barman

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arXiv · 2204.10311

Certain transformations and values of p-adic hypergeometric functions

Sulakashna·Rupam Barman

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Abstract

We prove two transformations for the $p$-adic hypergeometric functions which can be described as $p$-adic analogues of a Euler's transformation and a transformation of Clausen. We first evaluate certain character sums, and then relate them to the $p$-adic hypergeometric functions to deduce the transformations. We use a character sum identity proved by Ahlgren, Ono, and Penniston to deduce the $p$-adic Clausen's transformation. We also deduce special values of certain $p$-adic hypergeometric functions.

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Sulakashna, Rupam Barman. 2022-04-21. Certain transformations and values of p-adic hypergeometric functions. https://arxiv.org/abs/2204.10311

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