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Automatic discovery of irrationality proofs and irrationality measures. (English) Zbl 1468.11160
The paper deals with the irrationality measure exponents of the numbers \(\zeta(3)\), \(\zeta(2)\), \(\log 2\), the linear independence measure exponent of the numbers \(1\), \(\log 2\), \(\log 3\) and other results concerning for example special integrals. They do some discussions and, with the help of several algorithms, they propose preliminary calculations leading to the estimations of irrationality and linear independence measure exponents.
MSC:
11J82 Measures of irrationality and of transcendence
11J71 Distribution modulo one
11Y60 Evaluation of number-theoretic constants
33F10 Symbolic computation of special functions (Gosper and Zeilberger algorithms, etc.)
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