A distribution formula for Kashio's p-adic log-gamma function

Abstract

We study a special case of Kashio's p-adic log Gamma-function, that we call Log Gamma(p), which combines these of Morita and Diamond. It agrees with each of these on large parts of its domain and has the advantage of being a locally analytic function. We prove a distribution formula for Log Gamma(p) which generalizes and links the known distribution formulas for Diamond's and Morita's functions.