22
CRISTIANO HUSU
Proof. By Proposition 8.8.5 in [6], the expression (1.64) can be written
as
n ^^^r-^V (
L66
)
By induction on n (cf. Lemma 1.1 and Lemma 1.6), we assume that (1.66)
exists with n replaced by n 1. Then, the coefficient of
IKo1-''',
a,€Z,
1= 1
exists by inductive hypothesis and therefore (1.64) and (1.66) exist. The
existence of (1.65) is seen directly by means of the coefficient of
and without the need of induction.
The equality of the two expressions is seen in the same way as in the
proof of Lemma 1.6 (equality of (1.53) and (1.54)).
L e m m a 1.10 The expressions
Y{Y{. Y(Y(Y(vn, znm)Y(vn-U zn_1)TO)
)'"V2,z2i)vuz1y (1.67)
and
Y(Y(- Y(Y(Y(vn, znm)Y(vn.u zn.1m) •••
) ^771+ 1,771 )vm ? Zm—l,m—2
)--v2,z21)vuz1)- (1.68)
(n n
Tui'-^f1^))
n ^^{^-^A,
where 0 ra n, ezistf.
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