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, electromagnetics, and vibrations, where wave-like phenomena occur. These functions are defined for non-negative integer orders and exhibit oscillatory behavior, similar to sine and cosine functions. Unlike the first kind, J_n(x), Bessel Functions of the Second Kind can take on negative values and are singular at the origin for integer orders. They are essential for solving boundary value problems in cylindrical geometries.