FUNCTION : jac2prod - converts a product of theta functions into
q-product form.
CALLING SEQUENCE : jac2prod(jacexpr)
PARAMETERS : jacexpr - product of JAC(i,j, infinity)
where i,j are integers
and 0 < i < j.
=
SYNOPSIS :
jac2prod(jacexpr) returns a q-product;ie a product of the
a b
of functions of the form (q , q ) .
oo
EXAMPLES :
> x:=tripleprod(q,q^5,10);
99 70 46 27 13 4 7 18 34 55 81
x := q - q + q - q + q - q + 1 - q + q - q + q - q + q
> jacprodmake(x,q,50);
JAC(1, 5, oo)
> jac2prod(%);
5 4 5 5 5
(q, q ) (q , q ) (q , q )
oo oo oo
> XX:=series( (1- theta4(q,60)^2/theta4(q^5,12)^2)/4/q,q,60);
3 4 5 6 7 8 9 10 11 12
XX := 1 - q - q + q + 4 q - 4 q - q - 3 q + 3 q + 12 q - 12 q - 2 q
13 14 15 16 17 18 19 20
- 8 q + 8 q + 31 q - 30 q - 5 q - 20 q + 19 q + 72 q
21 22 23 24 25 26 27 28
- 68 q - 12 q - 44 q + 41 q + 154 q - 144 q - 24 q - 90 q
29 30 31 32 33 34 35
+ 84 q + 312 q - 289 q - 48 q - 178 q + 164 q + 603 q
36 37 38 39 40 41 42
- 554 q - 92 q - 336 q + 307 q + 1122 q - 1024 q - 168 q
43 44 45 46 47 48 49
- 612 q + 557 q + 2024 q - 1836 q - 300 q - 1087 q + 983 q
50 51 52 53 54 55 56
+ 3552 q - 3206 q - 522 q - 1880 q + 1692 q + 6088 q - 5472 q
57 58 59
- 886 q - 3180 q + O(q )
> jacprodmake(XX,q,50);
JAC(1, 10,oo) JAC(3, 10, oo)
----------------------------
2
JAC(5, 10, oo)
> jac2prod(%);
10 9 10 3 10 7 10
(q, q ) (q , q ) (q , q ) (q , q )
oo oo oo oo
------------------------------------------------------
5 10 4
(q , q )
oo
> JAC(0,10, infinity);
JAC(0, 10, oo)
> jac2prod(%);
10 10
(q , q )
oo
SEE ALSO : jac2series, prodmake, etamake