|
%I #11 Sep 08 2022 08:46:08
%S 2,6,5,8,6,4,9,5,8,2,7,9,3,0,6,9,8,2,6,9,1,8,7,5,0,8,6,3,9,7,1,2,0,6,
%T 8,7,6,4,2,7,8,3,8,2,3,9,7,5,1,3,8,9,9,9,3,8,0,5,9,7,4,1,5,3,2,8,5,7,
%U 4,3,9,5,1,3,0,2,7,7,1,1,4,0,5,4,4,1,1,4,0,7,0,3,2,0,5,7,7,1,7,4,0,4,5,7,1
%N Decimal expansion of Ti_2(2-sqrt(3)), where Ti_2 is the inverse tangent integral function.
%D Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 1.7.6 Inverse Tangent Integral, p. 57.
%H G. C. Greubel, <a href="/A244928/b244928.txt">Table of n, a(n) for n = 0..10000</a>
%H Eric Weisstein's MathWorld, <a href="http://mathworld.wolfram.com/InverseTangentIntegral.html">Inverse Tangent Integral</a>
%H Eric Weisstein's MathWorld, <a href="http://mathworld.wolfram.com/Polylogarithm.html">Polylogarithm</a>
%F 2/3*G + Pi/12*log(2-Sqrt(3)), where G is Catalan's number.
%F Also equals i/2*(polylog(2, -i*(2-sqrt(3))) - polylog(2, i*(2-sqrt(3)))), with i = sqrt(-1).
%e 0.26586495827930698269187508639712068764278382397513899938059741532857439513...
%t 2/3*Catalan + Pi/12*Log[2 - Sqrt[3]] // RealDigits[#, 10, 105]& // First
%o (PARI) default(realprecision, 100); (2/3)*Catalan + Pi/12*log(2 - sqrt(3)) \\ _G. C. Greubel_, Aug 25 2018
%o (Magma) SetDefaultRealField(RealField(100)); R:=RealField(); (2/3)*Catalan(R) + Pi(R)/12*Log(2 - Sqrt(3)); // _G. C. Greubel_, Aug 25 2018
%Y Cf. A006752, A244929.
%K nonn,cons,easy
%O 0,1
%A _Jean-François Alcover_, Jul 08 2014
|
