Raabe’s formula for -adic gamma and zeta functions
The classical Raabe formula computes a definite integral of the logarithm of Euler’s -function. We compute -adic integrals of the -adic -functions, both Diamond’s and Morita’s, and show that each of these functions is uniquely characterized by its difference equation and -adic Raabe formula. We also prove a Raabe-type formula for -adic Hurwitz zeta functions.