# bessel function

Solutions of Bessel's differential equation,

\[ x^2 \frac{d^2 y}{dx^2} + x \frac{dy}{dx} + \left(x^2 - \alpha^2 \right)y = 0 \]

This is the pdf of the product of two normal distributions.

A commonly used function is the 0th order Bessel function, defined

\begin{equation}
J_0 (x) = \frac{1}{\pi}\int_0^\pi e^{-jx \cos{\theta}}d\theta
\end{equation}