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Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!) A226654 Decimal expansion of the 1st Lebesgue constant L1. 5 1, 4, 3, 5, 9, 9, 1, 1, 2, 4, 1, 7, 6, 9, 1, 7, 4, 3, 2, 3, 5, 5, 9, 8, 6, 3, 2, 9, 9, 5, 9, 2, 7, 2, 2, 1, 6, 1, 2, 8, 1, 0, 6, 2, 9, 4, 0, 6, 6, 6, 1, 4, 6, 3, 8, 9, 3, 2, 0, 6, 5, 3, 7, 3, 9, 1, 5, 3, 9, 3, 9, 4, 0, 2, 7, 1, 8, 7, 2, 9, 2, 3, 0, 1, 4, 0, 9, 3, 3, 9, 0, 9, 7, 9, 6, 7, 5, 1, 1, 1, 7, 4, 8, 7 (list; constant; graph; refs; listen; history; text; internal format) OFFSET 1,2 COMMENTS Named after the French mathematician Henri Léon Lebesgue (1875-1941). - Amiram Eldar, Jun 19 2021 REFERENCES Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, page 251. LINKS Table of n, a(n) for n=1..104. Henri Lebesgue, Sur la représentation trigonométrique approchée des fonctions satisfaisant à une condition de Lipschitz, Bulletin de la Société Mathématique de France, Vol. 38 (1910), pp. 184-210. Eric Weisstein's MathWorld, Lebesgue constants. FORMULA Equals (1/Pi) * Integral_{t=0..Pi} abs(sin(3*t/2))/sin(t/2) dt. Equals 1/3 + 2*sqrt(3)/Pi. EXAMPLE 1.43599112417691743235598632995927221612810629406661463893206537391539394... MATHEMATICA RealDigits[1/3 + 2*Sqrt[3]/Pi, 10, 100][[1]] CROSSREFS Cf. A226655 (L2), A226656 (L3). Sequence in context: A227684 A200636 A229938 * A124451 A277261 A140391 Adjacent sequences: A226651 A226652 A226653 * A226655 A226656 A226657 KEYWORD cons,nonn AUTHOR Jean-François Alcover, Jun 14 2013 STATUS approved

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