FUNCTION : jac2series - converts a product of theta functions into
a product of q-series.
CALLING SEQUENCE : jac2series(jacexpr,T)
PARAMETERS : jacexpr - product of JAC(i,j, infinity)
where i,j are integers
and 0 < i < j.
=
SYNOPSIS :
jac2series(jacexp,T) returns a q-series product which agrees with
T
the function corresponding to jacexp to O(q ).
EXAMPLES :
> with(qseries):
> 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
> y:=jacprodmake(x,q,50);
y := JAC(1, 5, oo)
> jac2series(y,50);
4 7 13 18 27 34 46
1 - q - q + q + q - q - q + q + q
> 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
XX := 1 - q - q + q + 4 q - 4 q - q - 3 q + 3 q + 12 q - 12 q
12 13 14 15 16 17 18 19
- 2 q - 8 q + 8 q + 31 q - 30 q - 5 q - 20 q + 19 q
20 21 22 23 24 25 26 27
+ 72 q - 68 q - 12 q - 44 q + 41 q + 154 q - 144 q - 24 q
28 29 30 31 32 33 34
- 90 q + 84 q + 312 q - 289 q - 48 q - 178 q + 164 q
35 36 37 38 39 40 41
+ 603 q - 554 q - 92 q - 336 q + 307 q + 1122 q - 1024 q
42 43 44 45 46 47 48
- 168 q - 612 q + 557 q + 2024 q - 1836 q - 300 q - 1087 q
49 50 51 52 53 54 55
+ 983 q + 3552 q - 3206 q - 522 q - 1880 q + 1692 q + 6088 q
56 57 58 59
- 5472 q - 886 q - 3180 q + O(q )
> YY:=jacprodmake(XX,q,50);
JAC(1, 10, oo) JAC(3, 10, oo)
YY := ----------------------------------
2
JAC(5, 10, oo)
> JJ:=jac2series(YY,60);
96 57 28 9 12 33 64
JJ := (q - q + q - q + 1 - q + q - q + q )
88 51 24 7 3 16 39 72
(q - q + q - q + 1 - q + q - q + q )
/ 80 45 20 5 2
/ (2 q - 2 q + 2 q - 2 q + 1)
/
> series(JJ-XX,q,60);
59
O(q )
> Z:=JAC(0,10, infinity);
Z := JAC(0, 10, oo)
> jac2series(Z,50);
20 10 50
- q + 1 - q + q
SEE ALSO : jac2prod, jacprodmake