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. Author manuscript; available in PMC: 2013 Nov 6.
Published in final edited form as: Phys Rev E Stat Nonlin Soft Matter Phys. 2009 May 13;79(5 0 1):051908. doi: 10.1103/PhysRevE.79.051908

TABLE I.

Spherical harmonic multipole moments in terms of dipole density Ji

Dipole
a10 = ∫ d3 rJiz (r′)
a11 = ∫ d3 rJix (r′)
a11 = ∫ d3 rJiy (r′)
Quadrupole
a20 = ∫ d3 r′ [3zJiz (r′) − r′ · Ji(r′)]
a21 = ∫ d3 r′ [xJiz (r′) + zJix(r′)]
b21 = ∫ d3 r′ [yJiz (r′) + zJiy(r′)]
2a22 = ∫ d3 r′ [xJix (r′) − yJiy(r′)]
2b22 = ∫ d3 r′ [xJiy (r′) + yJix(r′)]