-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.