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

M2M translation formula

The multipole moment centred O' is given by (See (3.53) and (3.54))
M1j,n,m(O') = $\displaystyle \int_{S_y} C_{cdjl} \frac{\partial}{\partial y_l}
R_{n,m}(\overri...$ y $ }}) \phi_d(\mbox{\boldmath$ y $ }) n_c(\mbox{\boldmath$ y $ }) dS_{y} ,$ (H.1)
M2n,m(O') = $\displaystyle \int_{S_y} C_{cdjl} \frac{\partial}{\partial y_l}
...dmath$ y $ }}))\phi_d(\mbox{\boldmath$ y $ }) n_c(\mbox{\boldmath$ y $ }) dS_y.$ (H.2)

Substituting (E.2) into (H.1) we obtain

...-m'}(O)- (\overrightarrow{OO'})_j M^1_{j,n-n',m-m'}(O)\right).

Ken-ichi Yoshida