On transformation formulas of $p$-adic hypergeometric functions

Abstract

In this paper, we review hypergeometric functions $\mathscr{F}^{\rm Dw}_{\underline{a}}(t),$ $\mathscr{F}^{(σ)}_{\underline{a}}(t)$ and $\widehat{\mathscr{F}}^{(σ)} _{\mathbf{a}}(t)$ together with their conjectured transformation formulas, and show that one transformation formula implies the other.