## The irrationality measure of $$\pi$$ is at most 7.103205334137….(English)Zbl 1456.11129

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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