What exactly is modified about a modified Bessel function?

This article explores the meaning behind the term 'modified' in modified Bessel functions. It starts with the mathematical definition relating modified Bessel functions to standard Bessel functions via imaginary arguments, then explains the significance of this modification from both pure and applied perspectives. It highlights how modified Bessel functions arise in solving the heat equation in cylindrical coordinates, while standard Bessel functions appear in wave equation solutions. The article also touches on modified Struve functions, providing a clear understanding of the terminology and its practical relevance in physics and engineering.