Abstract:
We present a new proof of the irrationality
of values of the series
$$
\mathcal T_q(z)=\sum_{n=0}^\infty z^nq^{-n(n-1)/2}
$$
in both qualitative and quantitative forms. The proof is based on a hypergeometric construction of rational approximations to $\mathcal T_q(z)$.
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