[Calculation 14] q-Series and the q-Binomial Theorem

q-series and q-binomial theorem

In this post, we introduce q-Series and the q-Binomial theorem. For any complex number $a$, we write $$ (a;q)_k = (1-a)(1-aq)(1-aq^2) \cdots (1-aq^{k-1}) $$ where $|q|<1$. Also we write $$ (a;q)_\infty = \prod_{k=0}^\infty (1-aq^k). $$ With these notations, we will … Continue reading