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In astronomy, the spectral index of a source is a measure of the dependence of radiative flux density (that is, radiative flux per unit of frequency) on frequency. Given frequency ν {displaystyle u } and radiative flux density S ν {displaystyle S_{ u }} , the spectral index α {displaystyle alpha } is given implicitly by In astronomy, the spectral index of a source is a measure of the dependence of radiative flux density (that is, radiative flux per unit of frequency) on frequency. Given frequency ν {displaystyle u } and radiative flux density S ν {displaystyle S_{ u }} , the spectral index α {displaystyle alpha } is given implicitly by Note that if flux does not follow a power law in frequency, the spectral index itself is a function of frequency. Rearranging the above, we see that the spectral index is given by

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