Questions tagged [q-series]

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Finite version special case Jacobi triple product formula

In this paper, Shanks uses the following formula: $$ \sum_{s=0}^{n-1}q^{s(2n+1)} \times \left( \prod_{k=s+1}^{n} \dfrac{1-q^{2k}}{1-q^{2k-1}}\right) = \sum_{s=1}^{2n} q^{\frac{s(s-1)}{2}}$$ to get a ...
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Do asymptotic series at roots of unity uniquely determine a $q$-series?

Let $\{a_n\}_{n\geq 0}$ be a sequence of integers. We're interested in specific limits of the formal series $$f(q) = \sum_{n=0}^{\infty}a_n q^n.$$ Let $\zeta$ be a root of unity. Say $\zeta^k=1$. ...