On the integral involving product of modified Bessel functions of the first and second kinds

Abstract

In this paper, we introduce a new improper integral involving the product of modified Bessel functions of the first and second kinds. Our main objective is to investigate several analytical properties of (Formula presented.), including monotonicity, log-concavity, and geometrical concavity with respect to different parameters, and to establish new bounds for this function. A significant part of our analysis relies on known properties of the modified Bessel functions of the first and second kinds, as well as those of their product. © 2026 Informa UK Limited, trading as Taylor & Francis Group.