  We obtain the specific heat in the third constraint scenario for a canonical
ensemble of a nonextensive extreme relativistic ideal gas in a closed form. The
canonical ensemble of N particles in D dimensions is well-defined for the
choice of the deformation parameter in the range 0 < q < 1 + 1 / DN. For a
relativistic ideal gas with particles of arbitrary mass a perturbative scheme
in the nonextensivity parameter (1 - q) is developed by employing an infinite
product expansion of the q-exponential, and a direct transformation of the
internal energy from the second to the third constraint picture. All
thermodynamic quantities may be uniformly evaluated to any desired perturbative
order.
