FUNCTION : qseries[jacprod] - Jacobi-type infinite product
CALLING SEQUENCE : jacprod(a,b,q,T)
PARAMETERS : a,b positive integers
q variable
T - positive integer
SYNOPSIS :
T
jacprod(a,b,q,T) returns the q-series expansion to order O(q ) of
Jacobi-type infinite product
a b b-a b
(q , q ) (q , q )
oo oo
where a and b are positive integers and
q is a variable with |q|<1.
The expansion is found using qseries[tripleprod].
EXAMPLES :
-------------------------------------------------------------------------
> y:=series(1/jacprod(1,5,q,10),q,40);
2 3 4 5 6 7 8 9 10 11
y := 1 + q + q + q + 2 q + 2 q + 3 q + 3 q + 4 q + 5 q + 6 q + 7 q
12 13 14 15 16 17 18 19
+ 9 q + 10 q + 12 q + 14 q + 17 q + 19 q + 23 q + 26 q
20 21 22 23 24 25 26 27
+ 31 q + 35 q + 41 q + 46 q + 54 q + 61 q + 70 q + 79 q
28 29 30 31 32 33 34
+ 91 q + 102 q + 117 q + 131 q + 149 q + 167 q + 189 q
35 36 37 38 39 40
+ 211 q + 239 q + 266 q + 299 q + 333 q + O(q )
----------------------------------------------------------------------------
> x:=0:
----------------------------------------------------------------------------
> for i from 1 to 10 do x:=x+q^(i*i)/aqprod(q,q,i):od:
----------------------------------------------------------------------------
> series(x-y,q,50);
40
- 1 + O(q )
----------------------------------------------------------------------------
SEE ALSO :