Alternative Proof of Frullani's Theorem and Applications in Evaluating Frullani Integrals

Abstract

This article provides an alternative proof for the Frullani integral formula using an approach different from the existing one. This alternative proof gave us a novel method for evaluating certain improper integrals of Frullani type. Moreover, the alternative proof also obtained an exciting result relating the Frullani integral to a specific class of improper double integrals—the alternative proof started by stating and proving lemmas used as stepping stones to obtain the main proof. An essential condition was also imposed to obtain the desired result.