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%I #12 Sep 08 2022 08:46:08
%S 1,5,4,7,9,8,2,4,0,2,1,5,7,7,4,2,3,0,4,6,5,6,0,7,6,7,6,7,7,5,3,0,2,0,
%T 6,3,2,5,5,2,2,5,6,7,7,6,9,1,3,6,1,2,0,6,5,2,5,1,4,4,1,1,6,0,6,1,3,2,
%U 8,9,1,5,8,5,3,1,4,8,6,0,6,9,3,5,5,1,1,7,0,7,2,8,2,9,3,8,1,2,5,8,5,4,5,2,8
%N Decimal expansion of Integral_{x=0..Pi/2} (x^2/sin(x)) dx.
%D Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 1.7 Catalan's Constant, p. 57.
%H G. C. Greubel, <a href="/A245073/b245073.txt">Table of n, a(n) for n = 1..10000</a>
%H Eric Weisstein's MathWorld, <a href="http://mathworld.wolfram.com/AperysConstant.html">Apery's Constant</a>
%H Eric Weisstein's MathWorld, <a href="http://mathworld.wolfram.com/CatalansConstant.html">Catalan's Constant</a>
%F Equals 2*Pi*G - 7*zeta(3)/2, where G is Catalan's constant.
%F Also equals 4 * Integral_{x=0..1} (arctan(x)^2/x) dx.
%e 1.547982402157742304656076767753020632552256776913612065251441160613289...
%t RealDigits[2*Pi*Catalan - 7*Zeta[3]/2, 10, 105] // First
%o (PARI) default(realprecision, 100); 2*Pi*Catalan - 7*zeta(3)/2 \\ _G. C. Greubel_, Aug 24 2018
%o (Magma) SetDefaultRealField(RealField(100)); R:=RealField(); L:=RiemannZeta(); 2*Pi(R)*Catalan(R) - 7*Evaluate(L,3)/2; // _G. C. Greubel_, Aug 24 2018
%Y Cf. A002117, A006752.
%K nonn,cons,easy
%O 1,2
%A _Jean-François Alcover_, Jul 11 2014
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