C(m,r) = (-1)N'-- x (1/2L)Mk+1)-I Eq. 9.25
m n, n2 nk
CM) (( ... (. M
j jx m'r- .j n2'.- n j nr- ..
M M M M
mr, k) ni, n2j *** nk7,.r)
Note that the condition r- = 0 is implicitly asserted in this result by the form of the first
row of the combinatorial determinant, and that the condition ri e S" {0} for n # m is
enforced by the definition in Eq. 9.20.
When Eq. 9.25 is employed with Eq. 9.9, an additional simplification becomes
available. The simplification obtains by incorporating the factor
(1/2 L)q = 2A"
present in the Eq. 9.24 definition of C(m,r) with the product factor in Eq. 9.9. That is
-|PW- 1 = P-1| -IP--Il = YC(m,r) x n (P(i I n) 1/2L)i'
ir n S'ie S
= S C(m,r) x L x (2 L) I n n(P(i I n) 1/2L) Eq. 9.26
r (2 neE S i s
= C'(m,r)x H r (2LP(i n)-)
r ne S'ie S
where
C'(m, r) = C(m, r) x (1/2L)'I
is the coefficient of the indicated monomial in the new variables. Substitution of Eq. 9.25
into this expression for C'(m,r) yields