Hata, Masayoshi A note on Beukers’ integral. (English) Zbl 0830.11026 J. Aust. Math. Soc., Ser. A 58, No. 2, 143-153 (1995). The main result of this paper is the proof that \(\pi^2\) has an irrationality measure less than 6,3489. The last result was 7,325. The proof is based on expansions of so-called Beuker’s integrals. Reviewer: J.Hančl (Ostrava) Cited in 1 ReviewCited in 6 Documents MSC: 11J82 Measures of irrationality and of transcendence Keywords:\(\pi^ 2\); irrationality measure; Beuker’s integrals PDF BibTeX XML Cite \textit{M. Hata}, J. Aust. Math. Soc., Ser. A 58, No. 2, 143--153 (1995; Zbl 0830.11026)