MULTIPOLE MATRIX OF GREEN FUNCTION OF LAPLACE EQUATION

Multipole matrix of the Green function of the Laplace equation defined by double convolution of two spherical harmonics with the Green function of the Laplace equation is calculated. The multipole matrix elements in electrostatics describe potential on a sphere which is produced by a charge distributed on the surface of a different (possibly overlapping) sphere of the same radius. We calculate the multipole matrix from its Fourier trans-form. An essential part of our considerations is simplification of the three-dimensional Fourier transformation of a multipole matrix by its rotational symmetry to the one-dimensional Hankel transformation. DOI:10.5506/APhysPolB.46.1487 PACS numbers: 02.30.Uu, 41.20.C