  Using the exact computation of a large number of moments of the distribution
function of the end-to-end distance $G(r,N)$ of the worm-like chain, we have
established the analytical form of the coefficients in Taylor expansions of the
moments for short chain lengths $N$. The knowledge of these coefficients
enabled us to resummate the moment expansion of $G(r,N)$ by taking into account
consecutively the deviations of the moments from their stiff rod limit. Within
this procedure we have derived the short chain expansion for $G(r,N)$, the
scattering function, and the extension-force relation, which take into account
the deviations of the moments from their stiff rod limit to the seventh order
in $N$.
