Zeilberger, Doron; Zudilin, Wadim The irrationality measure of \(\pi\) is at most 7.103205334137…. (English) Zbl 1456.11129 Mosc. J. Comb. Number Theory 9, No. 4, 407-419 (2020). 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. Reviewer: Jaroslav Hančl (Ostrava) Cited in 4 Documents 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) Keywords:\( \pi \); irrationality measure exponent; experimental mathematics; Almkvist-Zeilberger algorithm PDF BibTeX XML Cite \textit{D. Zeilberger} and \textit{W. Zudilin}, Mosc. J. Comb. Number Theory 9, No. 4, 407--419 (2020; Zbl 1456.11129) Full Text: DOI arXiv References: [1] ; Alladi, J. Reine Angew. Math., 318, 137 (1980) · Zbl 0425.10039 [2] 10.1016/S0747-7171(08)80159-9 · Zbl 0717.33004 [3] 10.1112/blms/11.3.268 · Zbl 0421.10023 [4] 10.1007/BFb0093516 [5] 10.1016/0747-7171(92)90034-2 · Zbl 0754.05002 [6] 10.1515/crll.1990.407.99 · Zbl 0692.10034 [7] 10.1006/jnth.1993.1006 · Zbl 0776.11034 [8] 10.4064/aa-63-4-335-349 · Zbl 0776.11033 [9] ; Mahler, Nederl. Akad. Wetensch. Proc. Ser. A., 56, 30 (1953) · Zbl 0053.36105 [10] 10.24033/msmf.139 [11] 10.1007/BF03028234 · Zbl 0409.10028 [12] 10.4213/rm9175 [13] 10.4213/mzm8688 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.