  The two-dimensional one-component plasma (2dOCP) is a system of $N$ mobile
particles of the same charge $q$ on a surface with a neutralising background.
The Boltzmann factor of the 2dOCP at temperature $T$ can be expressed as a
Vandermonde determinant to the power $\Gamma=q^{2}/(k_B T)$. Recent advances in
the theory of symmetric and anti-symmetric Jack polymonials provide an
efficient way to expand this power of the Vandermonde in their monomial basis,
allowing the computation of several thermodynamic and structural properties of
the 2dOCP for $N$ values up to 14 and $\Gamma$ equal to 4, 6 and 8. In this
work, we explore two applications of this formalism to study the moments of the
pair correlation function of the 2dOCP on a sphere, and the distribution of
radial linear statistics of the 2dOCP in the plane.
