FUNCTION : qseries[etamake] - Convert a q-series into an eta-product expansion
CALLING SEQUENCE : etamake(f,q,T)
PARAMETERS : f - q-series
T - positive integers
SYNOPSIS :
etamake(f,q,T) converts the q-series f into an eta-product expansion
T
that agrees with f to O(q ).
EXAMPLES :
> tripleprod(q,q^3,10);
57 40 26 15 7 2 5 12 22 35 51
q - q + q - q + q - q + 1 - q + q - q + q - q + q
----------------------------------------------------------------------------
> etamake(%,q,20);
eta(tau)
--------
1/24
q
----------------------------------------------------------------------------
> sum((-1)^n*q^(n*n),n=-10..10);
100 81 64 49 36 25 16 9 4
2 q - 2 q + 2 q - 2 q + 2 q - 2 q + 2 q - 2 q + 2 q
- 2 q + 1
----------------------------------------------------------------------------
> etamake(%,q,50);
2
eta(tau)
----------
eta(2 tau)
----------------------------------------------------------------------------
SEE ALSO : qetamake