the Kelvin function

Kelvin functions are special mathematical tools used to solve complex problems involving wave patterns, heat transfer, or vibrations, especially when these involve circular or oscillatory behaviors. They are related to Bessel functions but are specifically adapted to handle situations where the behavior of a system changes with the distance or size, often involving imaginary or complex numbers. Think of Kelvin functions as a refined way to describe how certain physical processes evolve in circular or cylindrical systems, making them essential in engineering and physics for modeling real-world phenomena like electromagnetic waves or heat conduction in round objects.