## An elementary proof of the irrationality of Tschakaloff series.(English. Russian original)Zbl 1204.11112

J. Math. Sci., New York 146, No. 2, 5669-5673 (2007); translation from Fundam. Prikl. Mat. 11, No. 6, 59-64 (2005).
Summary: We present a new proof of the irrationality of values of the series $\mathcal{T}_q (z) = \sum\limits_{n = 0}^\infty {z^n q^{ - n(n - 1)/2}}$ in both qualitative and quantitative forms. The proof is based on a hypergeometric construction of rational approximations to $$\mathcal T_q (z)$$.

### MSC:

 11J72 Irrationality; linear independence over a field 11J91 Transcendence theory of other special functions

Chakalov series

### Citations:

JFM 48.0196.02; Zbl 0276.10020
Full Text:

### References:

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