Given $\tau\in H$ (up-half plane) and $q=e^{2\pi i \tau}$, Weber polynomail is defined as 


$$f(\tau)=q^{-\frac{1}{48}}\prod\_{i=0}^{\infty}(1+q^{i-\frac{1}{2}}).$$


My question is: How can I compute a product of unlimited sequence? Anyway, I have to finish $f(\tau)$ in finite steps. Of course, the faster the better. 



How to compute Weber polynomials efficiently?
An efficient construction of Weber polynomials, including a publicly available code, is given on page 340 and following of [On the Efficient Generation of Elliptic Curves over Prime Fields](https://www.ceid.upatras.gr/webpages/faculty/zaro/pub/conf/C29-ches2002-gen-ec.pdf) (2003).


