FPM 2005, vol. 11, no. 6, pp. 59-64

FUNDAMENTALNAYA I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

2005, VOLUME 11, NUMBER 6, PAGES 59-64

An elementary proof of the irrationality of Tschakaloff series

W. Zudilin

Abstract

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We present a new proof of the irrationality of values of the series

T_q(z) =
∑

_{n = 0}^∞ zⁿ q^{−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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Last modified: January 13, 2006