Whittaker-Shintani functions for Fourier-Jacobi models on unitary groups

We state and prove a formula for the Whittaker-Shintani functions associated to Fourier-Jacobi models for p-adic unitary groups and general linear groups. These generalized spherical functions play a fundamental role in the proof of the Gan-Gross-Prasad conjecture for Fourier-Jacobi models. As an application we prove the unramified Ichino-Ikeda conjecture.