  Thermodynamic quantities of Coulomb plasmas consisting of point-like ions
immersed in a compressible, polarizable electron background are calculated for
ion charges Z=1 to 26 and for a wide domain of plasma parameters ranging from
the Debye-Hueckel limit to the crystallization point and from the region of
nondegenerate to fully degenerate nonrelativistic or relativistic electrons.
The calculations are based on the linear-response theory for the electron-ion
interaction, including the local-field corrections in the electronic dielectric
function. The thermodynamic quantities are calculated in the framework of the
N-body hypernetted-chain equations and fitted by analytic expressions. We
present also accurate analytic approximations for the free energy of the ideal
electron gas at arbitrary degeneracy and relativity and for the excess free
energy of the one-component plasma of ions (OCP) derived from Monte Carlo
simulations.
  The extension to multi-ionic mixtures is discussed within the framework of
the linear mixing rule. These formulae provide a completely analytic, accurate
description of the thermodynamic quantities of fully ionized electron-ion
Coulomb plasmas, a useful tool for various applications from liquid state
theory to dense stellar matter.
