The function Y_n(x) is known as the Bessel function of the second kind, which is a solution to Bessel's differential equation. It is commonly used in various fields such as physics and engineering, particularly in problems involving cylindrical symmetry. The index n can be any real or complex number, and x is a non-negative real number. Bessel functions, including Y_n(x) , appear in applications like wave propagation, heat conduction, and vibrations. They are particularly useful in solving problems related to cylindrical coordinates and wave equations. The behavior of Y_n(x) is oscillatory and can be complex, especially for larger values of x .