On the gamma factor of the triple product L-functions

Let π1 and π2 be essentially (limit of) discrete series representations of GL2(R), and π3 be a principal series representation of GL2(R). We calculated the gamma factor of the triple product L-function L(s,π1×π2×π3) by constructing the normalized good sections and Whittaker functions for πi explicitly and showed that they coincide the functions which have been predicted by Langlands philosophy.