The refractive index of a Beutler-Fano resonance

We can recast equation (6.29) in frequency units v, to conform with the notation of Mitchell and Zemanski [283] (a standard reference for MOR) as 

For a discussion of the dispersion relations, see, e.g., Feynman [288], and for expressions related to equation (6.31), see Shore [289] who studies possible forms for the refractive index of an autoionising line, but does not give the q dependence of the coefficients in equation (6.31). 

In principle, there is a complication concerning constant or slowly-varying background terms which have been omitted from (6.31) in the simple form used here, the Kramers-Kronig relations are valid only for 

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