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 :