-F()) for p = 0 and that F(4 + r/2) = -F()) for p = 1. Thus
(Qe-2]) =0, (4-167)
(ii) i 0
The integrand F(4) (sin )") has the properties that F() = 1 for p = 0
and that F(4) + r) = -F(4) for p = 1. Thus, the only non-zero contribution
to Qa[C-2] comes from the case p = 0, i.e.
Qa [-2] P 3ARs. (4-168)
The significance of this analysis is that the non-vanishing A,-terms should al-
ov-iv take the form of Eq. (4-168) and therefore in calculating the regularization
parameters we need to sort out only this kind.
Then, we proceed with our calculations of the regularization parameters one
component at a time.
At-term:.
First we complete the expression for Qt[c-2] by recalling Eqs. (4-154) and
(4-155)
Qt [C-2] a(p2)
q2 [2 c + j2) x (2 + t cosO )]-32 (2E +2Js cos )
2 [(r + J2 21-2 + 2EJ sin O cos
q2E r2 A-3/2
X (2 + COS ) -3/2
2V2f (r2 + J2)5/2
q2EJX-3/2 cos -1/
q 2E E C 2)/ a (62 + 1- cos)-1/2 (4-169)
(r + J2)32 3/2
where a/0ae means that A is held constant while the differentiation is per-
formed with respect to 0.