  We consider correlation functions in one dimensional quantum integrable
models related to the algebra symmetries $\mathfrak{gl}(2|1)$ and
$\mathfrak{gl}(3)$. Using the algebraic Bethe Ansatz approach we develop an
expansion theorem, which leads to an infinite integral series in the
thermodynamic limit. The series is the generalization of the LeClair-Mussardo
series to nested Bethe Ansatz systems, and it is applicable both to one-point
and two-point functions. As an example we consider the ground state
density-density correlator in the Gaudin-Yang model of spin-1/2 Fermi
particles. Explicit formulas are presented in a special large coupling and
large imbalance limit.
