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The irrationality of \(\log(1+1/q) \log(1-1/q)\). (English) Zbl 0918.11040

The main result of this paper is the linear independence of numbers \[ \log(1+1/q),\quad \log(1-1/q),\quad\log(1+1/q)\log(1-1/q)\tag{1} \] over rational numbers for every natural number \(q\geq 1\). The estimations of the measure of linear independence are included too. The proofs are based on Padé approximation of Legendre polynomials.
Reviewer: J.Hančl (Ostrava)

MSC:

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

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