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M2L translation formula

Substituting (E.3) into (3.52) we obtain

\begin{eqnarray*}\lefteqn{ \sum_{n=0}^{\infty} \sum_{m=-n}^{n}
\left( \frac{\pa...
...box{\boldmath$ x $ }})
L^2_{n',m'}(\mbox{\boldmath$ x $ }_0),
\end{eqnarray*}


where $L^1_{j,n,m}(\mbox{\boldmath$\space x $ }_0)$ and $L^2_{n,m}(\mbox{\boldmath$\space x $ }_0)$ are the coefficients of the local expansion centred at $\mbox{\boldmath$\space x $ }_0$, given by

\begin{eqnarray*}L^1_{j,n,m}(\mbox{\boldmath$ x $ }_0)&=&\sum_{n'=0}^{\infty} \s...
...overrightarrow{O\mbox{\boldmath$ x $ }}_0)_j M^1_{j,n',m'}(O)).
\end{eqnarray*}




Ken-ichi Yoshida
2001-07-28