  This article is a companion to several works of the author and others on the
arithmetic of automorphic forms for GSp(4), and their associated L-functions
and Galois representations. These works require, at various points, an input
from smooth representation theory over p-adic local fields: the computation of
values of the unique trilinear form on an unramified representation of GSp(4) x
GL(2) x GL(2) invariant under the diagonal GL(2) x GL(2), for various different
input data. In this note, we carry out these local computations, using a
general formula for Shintani functions due to Gejima.
