Modified Bessel Functions
Modified Bessel Functions are special functions that arise in various problems of mathematical physics, particularly in situations involving cylindrical symmetry. They are denoted as I_n(x) and K_n(x), where n is the order of the function and x is a real or complex variable. These functions are solutions to the modified Bessel's differential equation, which is a variation of the standard Bessel equation.
These functions are commonly used in applications such as heat conduction, wave propagation, and in the study of electromagnetic fields. The modified Bessel functions exhibit exponential growth or decay, making them particularly useful in problems where boundary conditions are defined at infinity.