Mahler was the first to give an irrationality measure for pi,[6] in 1953.[7] Although some have suggested the irrationality measure of pi is likely to be 2, the current best estimate is 7.103205334137…, due to Doron Zeilberger and Wadim Zudilin.[8]
^Kurt Mahler, "Arithmetische Eigenschaften der Lösungen einer Klasse von Funktionalgleichungen", Math. Annalen, t. 101 (1929), p. 342–366.
^Kurt Mahler, "Arithmetische Eigenschaften einer Klasse von Dezimalbrüchen", Proc. Konin. Neder. Akad. Wet. Ser. A. 40 (1937), p. 421–428.
^Berggren, Lennart; Borwein, Jonathan M.; Borwein, Peter B.; Mahler, Kurt (2004). Pi, a source book. New York: Springer. pp. 306–318. ISBN0-387-20571-3. OCLC53814116.
^Kurt Mahler, "On the approximation of π", Nederl. Akad. Wetensch. Proc. Ser. A., t. 56 (1953), p. 342–366.
^Zeilberger, Doron; Zudilin, Wadim (5 November 2020). "The irrationality measure of π is at most 7.103205334137…". Moscow Journal of Combinatorics and Number Theory. 9 (4). Mathematical Sciences Publishers: 407–419. arXiv:1912.06345. doi:10.2140/moscow.2020.9.407. ISSN2640-7361. S2CID209370638.