We present explicit central value formulae for certain triple product L-functions over a totally real number field by using Ichino's formula. In particular, we carry out explicit computations for the local period integrals at the real defined in the Ichino's formula in very general settings. As applications, we first establish the rationality of the central critical values of these triple product L-functions. Base on this result, we prove the Deligne's conjecture for the central critical values of certain class of automorphic L-functions for GL(2)xGL(3).
