Symmetric absorbing-interval survival probability
= Symmetric absorbing-interval survival probability
{title2=$S(t)=\frac4\pi\sum_{j\ge0}\frac{(-1)^j}{2j+1}e^{-(2j+1)^2\pi^2Dt/(4L^2)}$}
For <diffusion> starting at the centre of $(-L,L)$ with absorbing endpoints, only even-parity spatial <eigenfunctions> contribute. Integrating their cosine expansion gives the displayed series. The leading late-time term has prefactor $4/\pi$ and decay rate $\pi^2D/(4L^2)$; its first relative correction is $-\frac13e^{-2\pi^2Dt/L^2}$.