Bessel function of the second kind

The Bessel function of the second kind, also called the Neumann function, is a mathematical function that arises when solving certain types of differential equations, especially those involving circular or cylindrical symmetry. These functions help describe wave patterns, vibrations, and fields in systems like antennas, optical fibers, or acoustics. While the Bessel functions of the first kind are common solutions, the second kind complements them to cover more complex boundary conditions. Think of them as tools to precisely model phenomena where circular or cylindrical shapes are involved, providing essential insights into their behavior and properties.