First, we describe our formulation for the double-layer potential. The
double-layer potential is written as

where

Substituting (3.142) into (3.162), we obtain

where and are the same as (3.147) and (3.148). In our formulation the number of the multipole moments is 4. Similarly, one can easily find that the number of the multipole moments for the single-layer potential is also 4.

Second, we describe Fujiwara's formulation for the double-layer potential.

Fujiwara's starting point is to write the fundamental solution
(3.139) as

Substituting (3.120) into (3.163), one obtains

where functions and are defined as

Substituting (3.164) into (3.162), one obtains

where and are defined as

Both and have three components. Therefore, the total number of the multipole moment for the double-layer potential is 6(=32) for a given pair of