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Decimal expansion of G/2 + (1/8)*Pi*log(2), where G is Catalan's constant (often also denoted K).
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%I #11 Aug 17 2020 13:12:40

%S 7,3,0,1,8,1,0,5,8,3,7,6,5,5,9,7,7,3,8,3,9,8,8,7,8,6,9,7,4,5,8,9,3,7,

%T 9,8,8,0,4,3,9,7,6,4,9,6,8,6,9,9,6,8,5,3,9,2,3,9,7,3,4,6,6,4,6,0,1,7,

%U 0,0,7,8,5,3,5,2,2,0,1,3,3,0,4,3,4,6,9,3,7,6,6,6,4,3,9,0,4,3,1,2

%N Decimal expansion of G/2 + (1/8)*Pi*log(2), where G is Catalan's constant (often also denoted K).

%D Jonathan Borwein, David Bailey and Roland Girgensohn, Experimentation in Mathematics: Computational Paths to Discovery, A K Peters, 2004, p. 20.

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/AhmedsIntegral.html">Ahmed's Integral</a>

%F Equals Integral_{x=0..1} arctan(x) / (x*(x^2+1)) dx.

%F From _Amiram Eldar_, Aug 17 2020: (Start)

%F Equals (1/2) * A006752 + A102886.

%F Equals Integral_{x=0..Pi/4} x*cot(x) dx. (End)

%e 0.7301810583765597738398878697...

%t RealDigits[Catalan/2 + Pi*Log[2]/8, 10 , 100][[1]] (* _Amiram Eldar_, Aug 17 2020 *)

%Y Cf. A006752, A102886, A096615, A102521.

%K nonn,cons,easy

%O 0,1

%A Mark Hudson (mrmarkhudson(AT)hotmail.com), Sep 08 2004