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An irrational number is a real number that cannot be expressed in the form $\frac{n}{m}$ where $n$ and $m$ are integers.

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A connection between basic hypergeometric series and number theory

I am studying functions given by the power series: $$f(z)=1+\sum_{n=1}^{\infty}\frac{z^n}{(1-q)(1-q^2)\cdots(1-q^{n})}.$$ The parameter $q$ is usually assumed to be such that $|q|<1$. Then it is easy …