Search: id:A088538
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%I A088538
%S A088538 1,2,7,3,2,3,9,5,4,4,7,3,5,1,6,2,6,8,6,1,5,1,0,7,0,1,0,6,9,8,0,1,1,4,8,
%T A088538 9,6,2,7,5,6,7,7,1,6,5,9,2,3,6,5,1,5,8,9,9,8,1,3,3,8,7,5,2,4,7,1,1,7,4,
%U A088538 3,8,1,0,7,3,8,1,2,2,8,0,7,2,0,9,1,0,4,2,2,1,3,0,0,2,4,6,8,7,6,4,8,5,8
%N A088538 Decimal expansion of 4/Pi.
%C A088538 Average length of chord formed from two randomly chosen points on the 
               circumference of a unit circle (see Weisstein/MathWorld link). - 
               Rick L. Shepherd (rshepherd2(AT)hotmail.com), Jun 19 2006
%C A088538 Suppose u(0)=1+i where i^2=-1 and u(n+1)=(1/2)*(u(n)+|u(n)|). Conjecture: 
               limit(Real(u(n)),n=+oo)=4/Pi. - Aktar Yalcin (aktaryalcin(AT)msn.com), 
               Jul 18 2007
%D A088538 S. R. Finch, Mathematical Constants, Encyclopedia of Mathematics and 
               its Applications, vol. 94, Cambridge University Press, p. 86
%H A088538 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               CircleLinePicking.html">Circle Line Picking</a>.
%H A088538 R. J. Mathar, <a href="http://arXiv.org/abs/math.CA/0403344">Chebyshev 
               Series Expansion of Inverse Polynomials</a>, arXiv:0403344 [math.CA]
%F A088538 4/Pi=prod(1-(-1)^((p-1)/2)/p) where p runs through the odd primes.
%F A088538 arcsin x = (4/Pi) sum_{n=1,3,5,7,...} T_n(x)/n^2 (Chebyshev series of 
               arcsin; App C of math.CA/0403344). - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), 
               Jun 26 2006
%e A088538 4/Pi=1.2732395....
%t A088538 RealDigits[N[4/Pi,6! ]][[1]] [From Vladimir Orlovsky (4vladimir(AT)gmail.com), 
               Jun 18 2009]
%Y A088538 Sequence in context: A124910 A090388 A021370 this_sequence A011049 A075639 
               A082737
%Y A088538 Adjacent sequences: A088535 A088536 A088537 this_sequence A088539 A088540 
               A088541
%K A088538 cons,nonn
%O A088538 1,2
%A A088538 Benoit Cloitre (benoit7848c(AT)orange.fr), Nov 16 2003
%E A088538 Updated arxiv reference - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), 
               Jul 22 2009

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