Expanding the polynomial under the integral ( ζ ζ + b ) l = ζ ζ l + l b ζ ζ l − − 1 + ⋯ ⋯ + l ζ ζ b l − − 1 + b l leads to the equation M k ′ ′ = M k + l b M k − − 1 + ⋯ ⋯ + l b l − − 1 M 1 + b l M 0 If the lower moments M k − − 1 , M k − − 2 , … … , M 1 , M 0 are zero, then M k ′ ′ = M k . The same equation shows that multipole moments higher than the first non-zero moment do depend on the choice of origin (in general).