## 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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