= K correction
{c}
{title2=$m_R=M_R+5\log_{10}(d_L/10\,\mathrm{pc})+K_R$}
{wiki}
The K-correction converts an observed <photometric passband> to a specified emitted <photometric passband>, accounting for <cosmological redshift> and the source spectrum. For a narrow same-band measurement, $K_R=-2.5\log_{10}[(1+z)L_\nu((1+z)\nu_R)/L_\nu(\nu_R)]$. Thus its sign depends on the spectrum, not on <redshift> alone. For $L_\nu\propto\nu^\alpha$, it is $-2.5(1+\alpha)\log_{10}(1+z)$. Finite-band corrections use the actual detector response and <magnitude zero point>.
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