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\(q\)-Apéry irrationality proofs by \(q\)-WZ pairs. (English) Zbl 0914.11042

The authors improve the irrationality measure of \[ \sum^\infty_{k=1} {1\over q^k- 1}\quad\text{and} \quad \sum^\infty_{n=1} {(1)^n\over q^n- 1} \] (\(q\) is an integer, \(| q|>1\)) to 4.80. The proofs use the so-called Apéry method of the irrationality of \(\zeta(3)\).
Reviewer: J.Hančl (Ostrava)

MSC:

11J82 Measures of irrationality and of transcendence
11J72 Irrationality; linear independence over a field
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References:

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