Modified Bessel functions are solutions to the modified Bessel's differential equation, which arise in various problems involving cylindrical symmetry, particularly when dealing with non-oscillatory phenomena. They differ from standard Bessel functions by their exponential behavior and are typically denoted as $$I_n(x)$$ and $$K_n(x)$$, where $$n$$ is the order of the function. These functions play a crucial role in mathematical physics, especially in contexts involving heat conduction, wave propagation, and potential theory.
congrats on reading the definition of modified bessel functions. now let's actually learn it.