Inversion transformation formula for Dwork's $p$-adic hypergeometric functions

Let $s\geq 1$ be an integer and let $a\in\mathbb{Z}_p$. Dwork's $p$-adic hypergeometric function is

$$\mathscr{F}^{{\rm Dw}}_{a_1,\cdots,a_s}(t):=\frac{F_{a_1,\cdots,a_s}(t)}{F_{a_1^\prime,\cdots,a_s^\prime}(t^p)},$$

where the numerator and denominator are hypergeometric power series. Suppose $a_1=\cdots=a_s=a$, and let $l$ be the unique integer in $\{0,1,\cdots,p-1\}$ such that $a+l\equiv 0\pmod p$. Then the inversion transformation formula is

$$\mathscr{F}^{{\rm Dw}}_{a,\cdots,a}(t)=((-1)^st)^l\mathscr{F}^{{\rm Dw}}_{a,\cdots,a}(t^{-1}).$$

This gives the inversion symmetry of Dwork's $p$-adic hypergeometric function when all parameters coincide; the supplied excerpt states the formula but does not provide a resolution status beyond its presentation as a conjectural candidate.