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)\; =\; \sum $_{n = 0}^{∞} z^{n}
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).

Location: http://mech.math.msu.su/~fpm/eng/k05/k056/k05606h.htm

Last modified: January 13, 2006