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A145960 Decimal expansion of 2*Log[5/3] = 1.0216... used by BBP Pi formula. 4

%I

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

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

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

%N Decimal expansion of 2*Log[5/3] = 1.0216... used by BBP Pi formula.

%C Equals 2*Log[5/3] = 2(Log[5]-Log[3]) = Log[25/9] = 4 ArcTanh[1/4] =

%C Hypergeometric2F1[1, 1/2, 3/2, 1/16] = Sum[(1/16)^n (1/(2n+1)),{n,0,Infinity}]

%C BBP Formula on Pi = 4*A145963-(1/2)A145960-(1/2)A145961-A145962 =

%C (*Artur Jasinski*) =4((1/16) (Pi + 4 ArcTan[1/3] + 4 Sqrt[2] ArcTan[1/Sqrt[2]] + Log[25] - 2 Sqrt[2] Log[2 - Sqrt[2]] + 2 Sqrt[2] Log[2 + Sqrt[2]]))-

%C (Sqrt[2] ArcCot[Sqrt[2]] + Sqrt[2] ArcCoth[Sqrt[2]] - Log[5]/2 - Pi/4 - ArcCot[3])-

%C (1/2)(2*Log[5/3])-

%C (1/2)(2*Log[3]-2 ArcTan[1/2]) =

%C Pi = 3.1414... = A000796

%H Eric W. Weisstein, <a href="http://mathworld.wolfram.com/BBPFormula.html">BBP Formula</a>

%H <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>

%t First[RealDigits[2 Log[5/3], 10, 100]]

%o (PARI) 2*log(5/3) \\ _Michel Marcus_, Apr 05 2015

%Y Cf. A000796, A145961, A145962, A145963.

%K cons,nonn

%O 1,3

%A _Artur Jasinski_, Oct 25 2008

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Last modified December 9 17:18 EST 2019. Contains 329879 sequences. (Running on oeis4.)