Abstract
The general mth-order, free-surface, multipole velocity potential is considered and found suitable for arrays of spherical devices requiring interactions between the devices. Expansions into an infinite series representation and an integral representation with finite limits are shown. These expressions can be evaluated by digital computer to any degree of accuracy and are formulated for especially rapid evaluation in certain regions: the series representation for small field distances, and the integral representation for large distances. Tables of the potentials and their Cartesian and radial derivatives are given to eight significant figures. Illustrations of multipoles between m = 0 and m = 4 are shown.
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