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An elementary proof of the irrationality of Tschakaloff series

Wadim Zudilin
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Abstract

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

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Wadim Zudilin. 2005-06-05. An elementary proof of the irrationality of Tschakaloff series. https://doi.org/10.1007/s10958-007-0382-0

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