Cox 



Q 



u^(x*,r*,5*) ^ -\t.\- jj S(r,^) I 



x*-e\ / ^* 



( r - r cos \p) dv 



Ml/2 ^g^j. 



" '+' jj Ap(r,0) 



Sk 



r 



'X /\ sin i// + — (v - X*) Xj. cos 



(All) 



3N ( r* - r cos >/;) 



dv 



d(9dr ^ , 



Q : 



X* 5X J- g^p, \p dv 



Mi/2 deidr 



+ jJ Ap(r,0) 



x*-^X /-\ cos [p + — (v - X*) \j. sin <// 



R..3 



3N^ r sin <p \ 

 + di 



d5dr> . 



(A12) 



APPENDIX B 

 SIMPLIFICATION OF DEFINITE INTEGRALS 



Simplification of U3(r*)p 



From Lerbs [14], Moriya [16], and others, Eq. (34) can be expressed as 



-a(r*)r=^/ 



1 f' dr(r) ^aC'-^-O 



dr (r* - r) 



by defining an induction factor ia(r*, r), where 



Q p-^ 



ijT*,r) -- r(r*-r) Z ^ J 



q- 1 



(Bl) 



dr 



(B2) 



954 



