The function K_n(x) is known as the modified Bessel function of the second kind, which is commonly used in various fields of mathematics and physics. It is defined for integer values of n and is particularly useful in solving problems involving cylindrical symmetry, such as heat conduction and wave propagation. The function K_n(x) exhibits exponential decay for large values of x and has a singularity at x = 0 for non-negative integers n . It is often encountered in applications related to Bessel functions, differential equations, and statistical mechanics.