FUNCTION : qseries[quinprod] - Watson's quintuple product
CALLING SEQUENCE : quinprod(a,b,q,T)
PARAMETERS : a,b,q - names
T - positive integer
or one of the names prodid or seriesid
SYNOPSIS :
CASE 1. T is a positive integer
T
quinprod(a,b,q,T) returns the q-series expansion to order O(q ) of
Watson's quintuple product
where z and q are real or complex variables (or constants) and
where z is nonzero and |q|<1.
Here T is postive integer.
The expansion is found using the quintuple product identity.
CASE 2. T = prodid
quinprod(a,b,q,prodid) returns the quintuple product identity
in product form.
CASE 3. T = seriesid
quinprod(a,b,q,prodid) returns the quintuple product identity
in series form.
EXAMPLES :
-------------------------------------------------------------------------
> quinprod(z,q,prodid);
2 2
(- z, q) (- q/z, q) (z q, q )
oo oo oo
q 2
(----, q ) (q, q) =
2 oo oo
z
2
q 3 3 3 3 3
(----, q ) (q z , q ) (q , q )
3 oo oo oo
z
q 3 2 3 3 3 3
+ z (----, q ) (q z , q ) (q , q )
3 oo oo oo
z
---------------------------------------------------------------------------
> quinprod(z,q,seriesid);
2 2
(- z, q) (- q/z, q) (z q, q )
oo oo oo
q 2
(----, q ) (q, q) =
2 oo oo
infinity
-----
\ (- 3 m) (3 m - 1) (1/2 m (3 m + 1))
) ((- z) - (- z) ) q
/
-----
m = - infinity
----------------------------------------------------------------------------
> quinprod(z,q,3);
/ 12 1 \ 22 / 9 1 \ 12 / 6 1 \ 5 / 3 1 \
|z + ---| q + |- z - ----| q + |z + ----| q + |- z - ----| q + 1 + z
| 11| | 8 | | 5 | | 2 |
\ z / \ z / \ z / \ z /
/ 1 4\ 2 / 1 7\ 7 / 1 10\ 15 / 1 13\ 26
+ |- ---- - z | q + |---- + z | q + |- ---- - z | q + |--- + z | q
| 3 | | 6 | | 9 | | 12 |
\ z / \ z / \ z / \z /
----------------------------------------------------------------------------
SEE ALSO :