Search: id:A145960
Results 1-1 of 1 results found.

%I A145960
%S A145960 1,0,2,1,6,5,1,2,4,7,5,3,1,9,8,1,3,6,6,4,1,1,0,2,8,1,9,2,6,0,7,3,2,3,8,
%T A145960 6,9,7,5,6,2,2,1,5,9,2,8,9,1,5,3,6,5,4,0,3,5,5,9,0,7,1,1,5,6,7,3,3,6,9,
%U A145960 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 A145960 Decimal expansion of 2*Log[5/3] = 1.0216... used by BBP Pi formula
%C A145960 A145960 = 2*Log[5/3] = 2(Log[5]-Log[3]) = Log[25/9] = 4 ArcTanh[1/4] 
               =
%C A145960 Hypergeometric2F1[1, 1/2, 3/2, 1/16] = Sum[(1/16)^n (1/(2n+1)),{n,0,Infinity}]
%C A145960 BBP Formula on Pi = 4*A145963-(1/2)A145960-(1/2)A145961-A145962 =
%C A145960 (*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 A145960 (Sqrt[2] ArcCot[Sqrt[2]] + Sqrt[2] ArcCoth[Sqrt[2]] - Log[5]/2 - Pi/4 
               - ArcCot[3])-
%C A145960 (1/2)(2*Log[5/3])-
%C A145960 (1/2)(2*Log[3]-2 ArcTan[1/2]) =
%C A145960 Pi = 3.1414... = A000796
%H A145960 Weisstein, Eric W., <a href="http://mathworld.wolfram.com/BBPFormula.html">
               BBP Formula.</a>
%p A145960 First[RealDigits[2 Log[5/3], 10, 100]]
%Y A145960 A000796, A145961, A145962, A145963
%Y A145960 Sequence in context: A128728 A084950 A066654 this_sequence A108767 A046817 
               A008970
%Y A145960 Adjacent sequences: A145957 A145958 A145959 this_sequence A145961 A145962 
               A145963
%K A145960 cons,nonn
%O A145960 1,3
%A A145960 Artur Jasinski (grafix(AT)csl.pl), Oct 25 2008

Search completed in 0.001 seconds