p-adic gamma function

Summary

The $p$-adic gamma function $\Gamma_p$ of Morita is a continuous function on the p-adic integers that plays the role of the gamma function. It interpolates a modified factorial in which the factors divisible by $p$ are left out. It satisfies a functional equation like $\Gamma(x+1) = x\,\Gamma(x)$, and it appears in the Gross–Koblitz formula for Gauss sums.