More generally, for sources at cosmological distances, a k-correction must be made for the spectral index α of the source, and a relativistic correction must be made for the fact that the frequency scale in the emitted rest frame is different from that in the observer's rest frame. So the full expression for radio luminosity, assuming isotropic emission, is L ν ν = S o b s 4 π π D L 2 ( 1 + z ) 1 + α α where L ν is the luminosity in W Hz, S obs is the observed flux density in W m Hz, D L is the luminosity distance in metres, z is the redshift, α is the spectral index (in the sense I ∝ ∝ ν ν α α , and in radio astronomy, assuming thermal emission the spectral index is typically equal to 2.)