We present an accurate analytic fitting formula for the numerical results for the relativistic corrections to the thermal Sunyaev-Zel ’ dovich 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 fitting is carried out for the ranges 0.02 \leq \theta _ { e } \leq 0.05 and 0 \leq X \leq 20 , where \theta _ { e } \equiv k _ { B } T _ { e } / m _ { e } c ^ { 2 } , X \equiv \hbar \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 .
The accuracy of the fitting is generally better than 0.1 % .
The present analytic fitting formula will be useful for the analyses of the thermal Sunyaev-Zel ’ dovich effect for high-temperature galaxy clusters .