Zeros of $p$-adic hypergeometric functions, $p$-adic analogues of Kummer's and Pfaff's identities

Neelam Saikia

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arXiv · 2001.01621

Zeros of $p$-adic hypergeometric functions, $p$-adic analogues of Kummer's and Pfaff's identities

Neelam Saikia

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Abstract

We classify all the zeros and non-zero values of a family of hypergeometric series in the $p$-adic setting. These values of hypergeometric series in the $p$-adic setting lead to transformations of hypergeometric series in the $p$-adic setting which can be described as $p$-adic analogues of Kummer's and Pfaff's linear transformations on classical hypergeometric series. We also evaluate certain summation identities for hypergeometric series in the $p$-adic setting as well as Gaussian hypergeometric series.

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Neelam Saikia. 2020-01-06. Zeros of $p$-adic hypergeometric functions, $p$-adic analogues of Kummer's and Pfaff's identities. https://arxiv.org/abs/2001.01621

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