Relativistic corrections to the Sunyaev-Zeldovich effect for extremely hot clusters of galaxies

We present an accurate numerical table for the relativistic corrections to the thermal Sunyaev-Zeldovich effect for clusters of galaxies. The numerical results for the relativistic corrections have been obtained by numerical integration of the collision term of the Boltzmann equation. The numerical table is provided for the ranges 0.002less than or equal totheta(e)less than or equal to0.100 and 0less than or equal toXless than or equal to20, where theta(e)equivalent tok(B)T(c)/m(e)c(2), Xequivalent to(h) over bar omega/k(B)T(0), T-e, is the electron temperature, omega is the angular frequency of the photon and T-0 is the temperature of the cosmic microwave background radiation. We also present an accurate analytic fitting formula that reproduces the numerical results with high precision.