FUNCTION :  qseries[qetamake] - convert q-series to a product of eta-functions
                                (variant of etamake) 

CALLING SEQUENCE : qetamake(f,q,T)
                    

PARAMETERS :   f    - q-series
               T  - positive integers

SYNOPSIS :
 qetamake is a variant of etamake.
 etamake(f,q,T) converts the q-series f into an eta-product expansion
                          T
 that agrees with f to O(q ).
 qetamake returns a product of the functions of the form _E(q^m)
 where _E(q) = (q;q)oo = (1-q)*(1-q^2)*(1-q^3)...
 In other words, _E(q) = eta(tau)/q^(1/24).

EXAMPLES :   

> with(qseries):
> A:=add(q^(n*(n+1)/2),n=0..20):
> etamake(A,q,20);
                                                 2
                                       eta(2 tau)
                                      -------------
                                       1/8
                                      q    eta(tau)

> qetamake(A,q,20);
                                             2 2
                                         _E(q )
                                         -------
                                          _E(q)



DISCUSSION :

SEE ALSO :  etamake