A closed-form formula for the Kullback-Leibler divergence between Cauchy distributions

We report a closed-form expression for the Kullback-Leibler divergence between Cauchy distributions which involves the calculation of a novel definite integral. The formula shows that the Kullback-Leibler divergence between Cauchy densities is always finite and symmetric.

💡 Research Summary

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The paper presents a complete closed‑form expression for the Kullback‑Leibler (KL) divergence between two Cauchy probability densities, each characterized by a location parameter (l) and a scale parameter (s). The authors start by recalling the standard Cauchy density
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