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

Paul Vincent Botin; Michael Sta. Brigida; Edwin  Balila

doi:10.70922/1xh6ay30

Authors

Paul Vincent E. Botin Cavite State University-Don Severino Delas Alas Campus, Indang 4122 Author
Michael E. Sta. Brigida University of the Philippines-Diliman, Diliman, Quezon City 1101 Author
Dr. Edwin A. Balila Adventist University of the Philippines, Puting Kahoy, Silang 4118, Cavite Author https://orcid.org/0000-0001-5153-7535 (unauthenticated)

DOI:

https://doi.org/10.70922/1xh6ay30

Keywords:

Double integral, Frullani integral, improper integral, Laplace transform

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.

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Author Biography

Dr. Edwin A. Balila, Adventist University of the Philippines, Puting Kahoy, Silang 4118, Cavite

Dean, College of Science and Technology, Adventist University of the Philippines, Puting Kahoy, Silang 4118, Cavite, Philippines 1008