Matter coupled F(4) gauged supergravity lagrangian

We construct the so far unknown lagrangian of D = 6, N = 2 F(4) Supergravit y coupled to an arbitrary number of vector multiplets whose scalars span th e coset manifold SO(4,n)/SO(4)xSO(n). This is done first in the ungauged ca se and then extended to the compact gauging of SU(2) x G, where SU(2) is th e R-symmetry diagonal subgroup of SU(2)(L) x SU(2)(R) similar or equal to S O(4) and G is a compact subgroup of SO(n), n being the number of vector mul tiplets, and such that dim( G) = n. The knowledge of the lagrangian allows in principle to refine the AdS(6)/CFT5 correspondence already discussed, as far as supersymmetric multiplets are concerned, in a previous related pape r. With respect to the latter we also give a more exaustive treatment of th e construction of the theory at the level of superspace Bianchi identities and in particular of the scalar potential.