Bessel Functions of the First Kind
Explore how Bessel order changes radial oscillation and the regular origin value.
Free theory articleExplore how Bessel order changes radial oscillation and the regular origin value.
Concept & interpretation
Bessel functions of the first kind, denoted as Jn(x), are solutions to Bessel's differential equation:x2y'' + xy' + (x2 - n2)y = 0. They frequently appear in physics and engineering problems, particularly those involving wave propagation and static potentials in cylindrical or spherical coordinate systems. The function Jn(x) for an integer order n can be expressed as a Taylor series around x = 0.
Experiment
In the interactive module below, you can select the order n and the probe location x. Observe how the value of the Bessel function changes and how the functions oscillate.
- Set "Order n" to 0 and "Probe x" to 0 to see that the function starts at 1.
- Set "Order n" to 1 or 2 and observe that the function starts at 0 for all other integer orders.
Try changing the order to n = 1 and note the root locations. Also, check out the full version at https://riano.app/module/bessel-functions-first-kind.