An elementary proof of the irrationality of Tschakaloff series

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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 $T_q(z)$.
5 pages, AMSTeX

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Number Theory, Classical Analysis and ODEs, 11J72, 11J82 (Primary), 33D15 (Secondary)

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http://salesiana.dossiersoluciones.com/handle/123456789/221219

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0506086
 http://arxiv.org/abs/math/0506086
 Fundam. Prikl. Mat. 11:6 (2005), 59--64; English transl., J. Math. Sci. 146 (2007), no. 2, 5669--5673
 doi:10.1007/s10958-007-0382-0

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arXiv