next up previous contents
Next: L2L translation formula Up: M2M, M2L, L2L in Previous: M2M translation formula

   
M2L translation formula

From (B.5) we obtain
 
$\displaystyle \overline{S_{n,m}}(\overrightarrow{O\mbox{\boldmath$ x $ }}) = \s...
...$ x $ }}) \overline{S_{n+n',m+m'}}(\overrightarrow{O\mbox{\boldmath$ x $ }_0}).$     (E.3)

Substituting (E.3) into (3.22) we have

\begin{eqnarray*}\lefteqn{
\sum_{n=0}^{\infty}\sum_{m=-n}^{n}\frac{\partial \ov...
...math$ x $ }})}{\partial n_x}
L_{n,m}(\mbox{\boldmath$ x $ }_0),
\end{eqnarray*}


where $L_{n,m}(\mbox{\boldmath$\space x $ }_0)$ is the coefficient of the local expansion centred at $\mbox{\boldmath$\space x $ }_0$ defined as

\begin{eqnarray*}L_{n,m}(\mbox{\boldmath$ x $ }_0)=\sum_{n'=0}^{\infty}\sum_{m'=...
...,m+m'}}(\overrightarrow{O\mbox{\boldmath$ x $ }_0})M_{n',m'}(O).
\end{eqnarray*}




Ken-ichi Yoshida
2001-07-28