The 𝑝-adic log gamma function and 𝑝-adic Euler constants

Abstract

We define G p {G_p} , a p-adic analog of the classical log gamma function and show it satisfies relations similar to the standard formulas for log gamma. We also define p-adic Euler constants and use them to obtain results on G p ′ G{’_p} and on the logarithmic derivative of Morita’s Γ p {\Gamma _p} .