** Next:** 6.1 Multipole Expansion
**Up:** On Convergence Acceleration of
** Previous:** 5 A Simple Example

We study the charge density of Eq.
(42) in the last section for
, and ,
where is the unit vector in *z* direction.
It is rotationally symmetric around the *z* axis. This density is also
plotted in
http://www.chemie.uni-regensburg.de/ECCC/4/rho.ps as a function of *x* and
*z* for *y*=0.
The corresponding electrostatic potential is also
rotationally symmetric around the *z* axis, a function of *z*
and only or, equivalently, only of
and with . This is also valid for the
multipole expansion (47) and the exact expansion
(45) in spherical harmonics.

** Next:** 6.1 Multipole Expansion
**Up:** On Convergence Acceleration of
** Previous:** 5 A Simple Example
Herbert H. H. Homeier (herbert.homeier@na-net.ornl.gov)