Cylindrical multipole moments
Cylindrical multipole moments are the coefficients in a series expansion of a potential that varies logarithmically with the distance to a source, i.e., as . Such potentials arise in the electric potential of long line charges, and the analogous sources for the magnetic potential and gravitational potential. For clarity, we illustrate the expansion for a single line charge, then generalize to an arbitrary distribution of line charges. Through this article, the primed coordinates such as refer to the position of the line charge(s), whereas the unprimed coordinates such as refer to the point at which the potential is being observed. We use cylindrical coordinates throughout, e.g., an arbitrary vector has coordinates where is the radius from the axis, is the azimuthal angle and is the normal Cartesian coordinate. By assumption, the line charges are infinitely long and aligned with the axis. (Wikipedia).
