may call differs from the index defined using The total flux between two frequencies or wavelengths is

which implies that

The opposite sign convention is sometimes employed, in which the spectral index is given by

The spectral index of a source can hint at its properties. For example, using the positive sign convention, the spectral index of the emission from an optically thin thermal plasma is -0.1, whereas for an optically thick plasma it is 2. Therefore, a spectral index of

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