Then, the rest of the argument is developed in the same way as in the ,in i,' -i of
Subsection 4.4.2. We categorize Qa[eo] in Eq. (4-231) into the following cases:
(i) i =2j +1 (j 0,1,2,...)
The integrand for "()" process, F(4) (sinF ) (cos 4)i = (sin 4)" (cos 4)2j+I
has the properties that F(4 + 7r) = -F(4) for p = even integers and that
F(4 + 7/2) = -F(4) for p = odd integers. Thus
(Qa[eo) = 0,
(4-232)
(ii) i 2j (j 0,1,2,...)
For p = odd integers, the integrand F(4))
that F(4 + 7r) F(4), hence
(sin 4)P (cos 4)2j has the property
(Qa[eo) = 0.
For p = even integers, using Eqs. (4-196), we have
Qa[e0] ~ (sin 4)p (cos 4)2j -(p/2+j)p 2(n-q)- lA2(n-q)+1 s,
(4-233)
(4-234)
where q = 0, 1, ,p + j is the index for a binomial expansion of (sin O)p+2j
and s = -2 for a t, r and s -1 for a = 0, 0. Here we can guarantee
that 2(n q) + 1 > 0 since 0 < q < +j = (p + i), 0 < i < k p and
p < k < 2n + 1. Then, Eq. (4-234) can be subcategorized into the following
two cases;
(ii-1) n q> 1
By Eqs. (4-155), (4-157) and (4-170)
Qa [e] ~ (sin 1)" (cos )2j X-(/2+j)-A 2 s 0,
where s -4 for a =t, r and s = -3 for a = 0, .
(4-235)