  This article proves a formula relating the multiplicity of an induced
representation and that of the inducing datum for the Bessel and the
Fourier-Jacobi models over Archimedean local fields by generalizing the
approach of C. Moeglin and J.-L. Waldspurger in [MW12], which was successful
for Bessel models of special orthogonal groups over non-Archimedean local
fields. As an application, we give a uniform proof of the local
Gan-Gross-Prasad conjecture for all classical groups over Archimedean local
fields for generic local $L$-parameters based on the tempered basic cases.
