1 . Introduction and Summary
Let q be fixed with Iql 1 and set
U )
n
=
1
(1.D U )
n
= (1a)(1aq)...(1aqn"1) = "n (1aqJ), n 1:
(a) = limo (a)n = n^ (1aq^).
njo j
= u
A l l of our r e s u l t s r e q u i r e t h a t no f a c t o r i n th e denominato r
v a n i s h e s . We have t h e expansion s
d.2) ^ i p
= 1
+
I
pf
,
yq
1,
2
oo n n
(1.3) = 1 + 1 y q
n=i ( y q )
n
( q ) n
0
2
oo n 2n  n ~ ,
(1.*) = 1 + 1 / ? , , (1yq
2 n
+
yq
3 n
)
and
( 1 . 5 ) ( x q ) „ = 1 • I
(

x )
"
q
.
2
n=i q )
n
, 2
n
^V^
00 ( ~ x ) n q ( x q )
n 1

( 1 . 6 ) = 1 + I _ HZ± ( 1  x q
2 n
)
n=i q)
n
R
2 ,
/ 5n 3n v
M 7
,
1
T ( " X ) P q 2 U q ) 2 ( n  1 )
M
3n 1 4n 2 6n 1 .
( 1 . 7 ) = 1 + i 1 1 ( 1  x q x q +x q )
n=i ( q )
n
Received by the editors January 12, 1983.