Abstract

Frullani’s Integral Formula is an old formula that was known to hold under strict conditions. Iyengar, and later Ostrowski, provided necessary and sufficient conditions for the existence of the Frullani Integral Formula. Their conditions were different but equivalent. In this article, we identify other conditions that are equivalent. We show that these conditions are, in fact, solutions to a family of linear differential equations of the first order. We study the limiting behavior of these solutions at zero and infinity, and in doing so, arrive at a new proof of the equivalence of Iyengar’s and Ostrowski’s conditions. Lastly, we provide applications of our results.