  We develop a direct approach to the semiclassical asymptotics for Bergman
projections in exponentially weighted spaces of holomorphic functions, with
real analytic strictly plurisubharmonic weights. In particular, the approach
does not rely upon the Kuranishi trick and it allows us to shorten and simplify
proofs of a result due to Rouby-Sj\"ostrand-V\~u Ngoc and Deleporte, stating
that in the analytic case, the amplitude of the asymptotic Bergman projection
is a realization of a classical analytic symbol.
