A226654 - OEIS

%I #15 Jun 19 2021 03:59:53

%S 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,

%T 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,

%U 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

%N Decimal expansion of the 1st Lebesgue constant L1.

%C Named after the French mathematician Henri Léon Lebesgue (1875-1941). - _Amiram Eldar_, Jun 19 2021

%D Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, page 251.

%H Henri Lebesgue, <a href="http://www.numdam.org/item/?id=BSMF_1910__38__184_0">Sur la représentation trigonométrique approchée des fonctions satisfaisant à une condition de Lipschitz</a>, Bulletin de la Société Mathématique de France, Vol. 38 (1910), pp. 184-210.

%H Eric Weisstein's MathWorld, <a href="http://mathworld.wolfram.com/LebesgueConstants.html">Lebesgue constants</a>.

%F Equals (1/Pi) * Integral_{t=0..Pi} abs(sin(3*t/2))/sin(t/2) dt.

%F Equals 1/3 + 2*sqrt(3)/Pi.

%e 1.43599112417691743235598632995927221612810629406661463893206537391539394...

%t RealDigits[1/3 + 2*Sqrt[3]/Pi, 10, 100][[1]]

%Y Cf. A226655 (L2), A226656 (L3).

%K cons,nonn

%O 1,2

%A _Jean-François Alcover_, Jun 14 2013