  We calculate holographically one and two-point functions of scalar operators
at finite density and/or finite temperature. In the case of finite density and
zero temperature we argue that only scalar operators can have non-zero VEVs. In
the case in which both the chemical potential and the temperature are finite,
we present a systematic expansion of the two-point correlators in powers of the
temperature T and the chemical potential $\Omega$.
  The holographic result is in agreement with the general form of the OPE which
dictates that the two-point function may be written as a linear combination of
the Gegenbauer polynomials $C_J^{(1)}(\xi)$ but with the coefficients depending
now on both the temperature and the chemical potential, as well as on the CFT
data. The leading terms in this expansion originate from the expectation values
of the scalar operator $\phi^2$, the R-current ${\cal J}^\mu_{\phi_3}$ and the
energy-momentum tensor $T^{\mu\nu}$.
  By employing the Ward identity for the R-current and by comparing the
appropriate term of the holographic result for the two-point correlator to the
corresponding term in the OPE, we derive the value of the R-charge density of
the background. Compelling agreement with the analysis of the thermodynamics of
the black hole is found. Finally, we determine the behaviour of the two-point
correlators, in the case of finite temperature, and in the limit of large
temporal or spatial distance of the operators.
