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Hill's Differential Equation


\begin{displaymath}
{d^2x\over dt^2}=\phi(t)x,
\end{displaymath}

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

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

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

See also Hill Determinant




© 1996-9 Eric W. Weisstein
1999-05-25