- x2y'' + xy' + (x2 - n2)y = 0
for non-negative integer values of n.
They come in two kinds:
- Bessel functions of the first kind Jn(x), the solutions of the above differential equation which are defined for x = 0.
- Bessel functions of the second kind Yn(x), the solutions which are non-singular (infinite) for x = 0.
The graphs of Bessel function look like oscillating sine or cosine functions which "level off" because they have been divided by a term of the order of √x.