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

We study a special case of Kashio's p-adic log⁡Γ-function, that we call LogΓp, 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 LogΓp which generalizes and links the known distribution formulas for Diamond's and Morita's functions.