FUNCTION : qseries[winquist] - q-series of Winquist's product
CALLING SEQUENCE : winquist(a,b,q,T)
PARAMETERS : a,b,q - names
T - positive integer
SYNOPSIS :
T
winquist(a,b,q,T) returns the q-series expansion to order O(q ) of
Winquist's product
2
(a;q) (q/a;q) (b;q) (q/b;q) (ab;q) (q/(ab);q) (a/b;q) (b/(aq);q) (q;q)
oo oo oo oo oo oo oo oo oo
where a,b and q are real or complex variables (or constants) and
where a,b are nonzero and |q|<1.
Here T is postive integer. The expansion is found using Winquist's
identity.
EXAMPLES :
> winquist(a,b,q,30)/(1-a)/(1-b)/(1-a*b)/(1-a/b):
> normal(series(%,q,30)):
> subs(a=1,b=1,%);
2 3 4 5 7 8 9 10
1 - 10 q + 35 q - 30 q - 105 q + 238 q - 260 q - 165 q + 140 q + 1054 q
11 12 14 15 16 18 19
- 770 q - 595 q - 715 q + 2162 q + 455 q - 2380 q - 1820 q
20 21 22 23 24 25 26
+ 2401 q - 680 q + 1495 q + 3080 q + 1615 q - 6958 q - 1925 q
29 30
+ 5100 q + O(q )
> series(% - tripleprod(q,q^3,10)^10,q,30);
30
O(q )
SEE ALSO :