16 



and 



//P. P±l) 



f {Pl+l^n^^ {l-(i^){n+l)^ +p(p±l)T(n + l){2p±l)] 



//TV 



p p+ 1 



fi afi 



The convention is adopted in Equation [29] that 



6° = 6° =0 

 n n 



These integrals are evaluated in Appendix 1. The components of Fj become 



oo n 



[30a] 



n=o s=o 



' „ -^"^ \ / (n - s - ly 



n 

 - yr,(s)(a^+ia^ + 6^+1 ? Vn+ s + 2)] 



[30b] 



oo P n— 1 



n=o s=o 

 n 



[30c] 



These components must be evaluated at each singularity. F^ is then given by Equation [20]. 

 The Equations [30] are bilinear forms in the coefficients of the expansion of the total 

 potential, excluding the singularity, and coefficients of the expansion due to the singularity. 

 The bilinear character of these expressions has a number of important consequences: 



