Archimedean zeta integrals on U(n,1)

For a dual pair of unitary groups with equal size, zeta integrals arising from Rallis inner product formula give the central values of certain automorphic L  -functions. In this paper we explicitly calculate archimedean zeta integrals of this type for U(n,1)U(n,1), assuming that the corresponding archimedean component of the automorphic representation is a holomorphic discrete series.