Radiative heat flux \( \dot{q} \) at a hot surface at a temperature \( T_s \) can be expressed as \[ \dot{q} = A f(T_s, T_\infty) (T_s - T_\infty) \] where \( A \) is a constant and \( T_\infty \) is the temperature of the surroundings (temperatures are expressed in K). The function \( f(T_s, T_\infty) \) is given by ______.