For p = even integers, using Eqs. (4-196), we have
Qa [e] ~ (sin 4)" (cos 4)2J X-(/2+j)p 2(n-q)- I2(n-q)+2s, (4-244)
where q = 0,1, p + j is the index for a binomial expansion of (sin 8)p+2j
as seen in Eq. (4-196) and s -3 for a = t,r and s = -2 for a = 0, It is
guaranteed that 2(n q)+2 > 0 or n -q > -1 since 0 < q < p+j (p+ i),
0 < i < k p and p < k < 2n + 2. Then, Eq. (4-244) can be subcategorized
into the following three cases;
(ii-1) n- q> 1
By Eqs. (4-155), (4-157) and (4-170)
Qa[e1] (sin 4)"P(cos4)2J -(p/2+j)A 3 -- 0, (4-245)
where s = -5 for a t, r and s = -4 for a 0, .
(ii-2) n q 0
By Eqs. (4-155), (4-157) and (4-171)
Qa [1] ~ (sin 4)" (cos 4)2J -(p/2+j)A2 2s-- 0, (4-246)
where s -4 for a =t, r and s = -3 for a = 0, .
(ii-3) n- q -1
We have
Qa [1] ~ (sin 4)" (cos 4)2j x-(p/2+j)&os, (4-247)
where s = -3 for a t, r and s = -2 for a .
Therefore, through the analysis we find that the non-vanishing Qa[I1] results only
from the case of n-q = -1 in the form of Eq. (4-247). By 0 < q < +p+j (p+i),