Hill's Differential Equation

$${d^2x\over dt^2}=\phi(t)x,$$

where $\phi$ is periodic. It can be written as

$${d^2y\over dx^2} +\left[{\theta_0+2\sum_{n=1}^\infty \theta_n\cos(2nz)}\right]= 0,$$

where $\theta_n$ are known constants. A solution can be given by taking the ``Determinant'' of an infinite Matrix.

See also Hill Determinant