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M2M translation formula

The multipole moment centred O' is given by (See (3.128))
 
$\displaystyle M_n^m(k,O') = \int_{S_y} \frac{\partial }{\partial n_y }
\overlin...
...k,\overrightarrow{O'\mbox{\boldmath$ y $ }}) \phi(\mbox{\boldmath$ y $ }) dS_y.$     (I.1)

Substituting (3.123) into (I.1), we obtain the following M2M translation formula:

\begin{eqnarray*}\lefteqn{M_n^m(k,O')}\nonumber \\
&=& \int_{S_y} \frac{\partia...
...
{\cal I}_l^{-m-m'}(k,\overrightarrow{O'O}) M_{n'}^{-m'}(k,O).
\end{eqnarray*}




Ken-ichi Yoshida
2001-07-28