Bessel Functions of the second kind, denoted as Y_n(x), are solutions to Bessel's differential equation that arise in various physical problems, particularly in cylindrical coordinates. They are important in fields such as acoustics, electromagnetism, and vibrations, where wave-like phenomena occur. These functions are characterized by their oscillatory behavior and singularity at the origin for integer orders. Unlike the first kind, J_n(x), which are finite at the origin, Bessel Functions of the second kind are used to describe boundary conditions in problems involving cylindrical symmetry, making them essential in mathematical physics.