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%I #11 Sep 08 2022 08:46:08
%S 2,3,3,4,5,3,7,5,8,5,3,1,2,3,4,1,1,4,6,7,5,9,0,3,8,6,2,7,7,4,3,9,3,3,
%T 0,0,4,8,8,2,6,7,8,3,7,7,2,5,0,9,9,3,5,4,0,1,6,3,0,0,5,4,0,1,8,4,4,1,
%U 8,0,1,0,3,4,5,3,6,3,3,5,0,7,6,4,5,3,6,9,0,1,6,5,4,4,1,7,1,8,3,7,9,7,1,4,4
%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="/A244929/b244929.txt">Table of n, a(n) for n = 1..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 + 5*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 2.3345375853123411467590386277439330048826783772509935401630054018441801...
%t 2/3*Catalan + 5*Pi/12*Log[2 + Sqrt[3]] // RealDigits[#, 10, 105]& // First
%o (PARI) default(realprecision, 100); 2/3*Catalan + 5*Pi/12*log(2 + sqrt(3)) \\ _G. C. Greubel_, Aug 25 2018
%o (Magma) SetDefaultRealField(RealField(100)); R:=RealField(); (2/3)*Catalan(R) + 5*Pi(R)*Log(2 + Sqrt(3))/12; // _G. C. Greubel_, Aug 25 2018
%Y Cf. A006752, A244928.
%K cons,easy,nonn
%O 1,1
%A _Jean-François Alcover_, Jul 08 2014
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