  We present an exact many-body theory of ultracold fermionic gases for the
Bose-Einstein condensation (BEC) regime of the BEC-BCS crossover. This is a
purely fermionic approach which treats explicitely and systematically the
dimers formed in the BEC regime as made of two fermions. We consider
specifically the zero temperature case and calculate the first terms of the
expansion of the chemical potential in powers of the density $n$. We derive
first the mean-field contribution, which has the expected standard expression
when it is written in terms of the dimer-dimer scattering length $a_M$. We go
next in the expansion to the Lee-Huang-Yang order, proportional to $n^{3/2}$.
We find the far less obvious result that it retains also the same expression in
terms of $a_M$ as for elementary bosons. The composite nature of the dimers
appears only in the next term proportional to $n^2$.
