Search: id:A094640
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%I A094640
%S A094640 2,4,1,5,6,4,4,7,5,2,7,0,4,9,0,4,4,4,6,9,1,0,3,6,8,9,1,5,6,3,2,9,4,4,2,
%T A094640 4,5,0,3,7,0,5,4,5,5,8,0,5,1,9,8,9,3,6,7,2,7,7,3,6,9,4,7,5,1,4,6,4,9,4,
%U A094640 7,4,0,5,4,5,6,3,3,5,1,4,2,8,1,0,3,3,8,3,7,1,7,3,4,7,6,6,7,3,8,1,9,9,3
%N A094640 Decimal expansion of log 4/Pi.
%C A094640 Decimal expansion of Integrate[(x - 1)/((1 + x y) Log[x y]),{y,0,1},{x,
               0,1}]. - Jonathan Sondow (jsondow(AT)alumni.princeton.edu), Jan 27 
               2005
%D A094640 G. Boros and V. Moll, Irresistible Integrals: Symbolics, Analysis and 
               Experiments in the Evaluation of Integrals, Cambridge University 
               Press, Cambridge, 2004, Chap. 7.
%D A094640 J. Borwein and P. Borwein, Pi and the AGM, John Wiley & Sons, New York, 
               1987, Chap. 11.
%D A094640 D. Huylebrouck, Similarities in irrationality proofs for Pi, ln2, zeta(2) 
               and zeta(3), Amer. Math. Monthly 108 (2001) 222-231.
%D A094640 J. Sondow, Double Integrals for Euler's Constant and ln(4/Pi) and an 
               Analog of Hadjicostas's Formula, Amer. Math. Monthly 112 (2005) 61-65.
%H A094640 J. Sondow, <a href="http://arXiv.org/abs/math.CA/0211148">Double Integrals 
               for Euler's Constant and ln(4/Pi)</a>.
%H A094640 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               Euler-MascheroniConstant.html">Euler-Mascheroni Constant</a>
%H A094640 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               HadjicostassFormula.html">Hadjicostas's Formula</a>
%H A094640 J. Sondow, <a href="http://arXiv.org/abs/math.NT/0508042">New Vacca-Type 
               Rational Series for Euler's Constant and Its "Alternating" Analog 
               ln(4/Pi)</a>
%H A094640 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               DigitCount.html">Digit Count</a>
%e A094640 log(4/Pi) = 0.24156447527...
%t A094640 RealDigits[ Log[4/Pi], 10, 111][[1]]
%Y A094640 Cf. A094641. See also A103130.
%Y A094640 Cf. A110625, A110626.
%Y A094640 Sequence in context: A060370 A165064 A021418 this_sequence A070937 A059573 
               A080427
%Y A094640 Adjacent sequences: A094637 A094638 A094639 this_sequence A094641 A094642 
               A094643
%K A094640 cons,easy,nonn
%O A094640 0,1
%A A094640 Jonathan Sondow (jsondow(AT)alumni.princeton.edu) and Robert G. Wilson 
               v (rgwv(AT)rgwv.com), May 18 2004

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