An elementary proof of the irrationality of Tschakaloff series
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🧮 math.NT
math.CA
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proofirrationalityseriesapproximationsconstructionelementaryformshypergeometric
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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 $T_q(z)$.
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