Then, our Ba-terms are read off from the coefficient of the sum Z7o 1,
Ba = Y/3nm(a) F-(-n-la/2), (4-209)
n=1,2 m0
where the identity (X-p) Fp 2F 2 ; 1; J2/( + J2)) was taken from
Appendix C of Ref. [18].
Below are presented the calculations of B,-terms of the regularization parame-
ters by component.
Bt-term:.
We begin with
1 t(IIIt=t] 3 [dtP(2 IIIIt t=to (4-210)
Qt[C -1] q2 1tTPi t 4 3 [ (4-210)
2 p0 0
The subsequent computation will be very lengthy and it will be reasonable to split
Qt[c-1] into two parts. First, let
2
Qt(1) [ ] -- 3 ,tP III t to' (4-211)
where
MEtA2 ( M EJA
tit f22 2 1 ( 0 o)
0 f' f 0
+roEt (- o)2+ (- )2 (4-212)
As proved at the beginning of this Subsection, every (0 ko)" in the numerators of
the e-1 term can be replaced by (0 (')" without affecting the rest of calculation.
Then, followed by the rotation of the coordinates via Eq. (4-151)
q2 MEtA2 / E JA
Qt(1) [-1 = 3 2 -- 23 1 sin O cos )
Sf o 0 f o
+ 2roE (t cos 0)
+0 (X o) (4-213)
L(4-M)
0