Congruence relations for $p$-adic hypergeometric functions $\widehat{\mathscr{F}}_{a,...,a}^{(\sigma)}(t)$ and its transformation formula

Wang Chung-Hsuan

doi:10.1007/s00229-021-01327-1

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arXiv · 2001.08117

Congruence relations for $p$-adic hypergeometric functions $\widehat{\mathscr{F}}_{a,...,a}^{(\sigma)}(t)$ and its transformation formula

Wang Chung-Hsuan

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Abstract

We introduce new kind of $p$-adic hypergeometric functions. We show these functions satisfy congruence relations, so they are convergent functions. And we show that there is a transformation formula between our new $p$-adic hypergeometric functions and $p$-adic hypergeometric functions of logarithmic type defined by M. Asakura in a particular case.

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Wang Chung-Hsuan. 2020-01-20. Congruence relations for $p$-adic hypergeometric functions $\widehat{\mathscr{F}}_{a,...,a}^{(\sigma)}(t)$ and its transformation formula. https://doi.org/10.1007/s00229-021-01327-1

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