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L2L translation formula

Substituting (E.4) into (3.59) we obtain

\begin{eqnarray*}\lefteqn{\sum_{n=0}^{\infty} \sum_{m=-n}^{n}
\left( \frac{\par...
...box{\boldmath$ x $ }})
L^2_{n',m'}(\mbox{\boldmath$ x $ }_1),
\end{eqnarray*}


where $L^1_{j,n,m}(\mbox{\boldmath$\space x $ }_1)$ and $L^2_{n,m}(\mbox{\boldmath$\space x $ }_1)$ are the coefficients of the local expansion centred at $\mbox{\boldmath$\space x $ }_1$, given by

\begin{eqnarray*}L^1_{j,n,m}(\mbox{\boldmath$ x $ }_1)&=&\sum_{n'=n}^{\infty} \s...
...boldmath$ x $ }_1})_j L^1_{j,n',m'}(\mbox{\boldmath$ x $ }_0)).
\end{eqnarray*}




Ken-ichi Yoshida
2001-07-28