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The irrationality measure of \(\pi\) is at most 7.103205334137…. (English) Zbl 07272358
The main result of this paper is that the irrationality measure exponent of the number \(\pi\) is less than \(7.103205334138\). The proof uses complex analysis, is based on clever calculating of special integral and is in the spirit of Salikov.
MSC:
11J82 Measures of irrationality and of transcendence
11Y60 Evaluation of number-theoretic constants
33F10 Symbolic computation of special functions (Gosper and Zeilberger algorithms, etc.)
33C60 Hypergeometric integrals and functions defined by them (\(E\), \(G\), \(H\) and \(I\) functions)
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