P-adic gamma function

In mathematics, the p-adic gamma function Γ_p(s) is a function of a p-adic variable s analogous to the Gamma function.

Definition

The p-adic gamma function is the unique continuous function of a p-adic integer s such that

$\Gamma _{p}(s)=(-1)^{s}\prod _{0<i<s,p\not {|}i}i$

for positive integers s.