An approximation of Planck´s formula for the inverse black body radiation problem

A modification to the Hamid-Ragheb approximation leads to a new approximate formula for the Planck´s radiation law valid at all frequencies. The modified regime is useful in solving the inverse black body radiation problem in closed form. The absolute percentage errors in constructing the area-coldness distribution due to the proposed and previous approximations are presented. The results suggest that our modified approximation to Planck´s law is more suitable than all other approximations at all frequencies.