Bessel Functions
A family of canonical special functions J_α(x) and Y_α(x) serving as solutions to Bessel's differential equation.
Governing formula
x² y'' + x y' + (x² - α²) y = 0 ⇒ y(x) = A J_α(x) + B Y_α(x)
SI unit
Cylindrical Special Functions
In depth
Arise naturally when solving Laplace, Helmholtz, or wave equations in cylindrical or spherical geometry coordinates.
Examples in the real world
Calculating transverse electric (TE) and magnetic (TM) wave modes in cylindrical wave guides and circular drumhead vibrations.