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How can I determine the Cauchy principle value in Kramers Kronig relations (KK)?

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m.mohamed

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Hello Dears
I use the kramers kronig (KK) relations to demonstrate the arbitrary values of the dielectric constant with the measured values, but in the derivation of KK relations, there is a Cauchy value P as shown below, but I dont know how to determine its value.
img2.gif

Is there anybody have an expertise with such an equation or in general Cauchy value?
 

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