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A088538
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Decimal expansion of 4/Pi.
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28
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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, 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, 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
(list; constant; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| 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
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
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REFERENCES
| S. R. Finch, Mathematical Constants, Encyclopedia of Mathematics and its Applications, vol. 94, Cambridge University Press, p. 86
L. B. W. Jolley, Summation of Series, Dover (1961).
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LINKS
| Eric Weisstein's World of Mathematics, Circle Line Picking.
R. J. Mathar, Chebyshev Series Expansion of Inverse Polynomials, arXiv:0403344 [math.CA]
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FORMULA
| 4/Pi=prod(1-(-1)^((p-1)/2)/p) where p runs through the odd primes.
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, Jun 26 2006
Equals 1+sum_{n>=1} ((2n-3)!!/(2n)!!)^2. [Jolley eq 274] - R. J. Mathar, Nov 03 2011
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EXAMPLE
| 4/Pi=1.2732395.... = 1/0.78539816...
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MATHEMATICA
| RealDigits[N[4/Pi, 6! ]][[1]] [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Jun 18 2009]
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CROSSREFS
| Cf. A079097 for terms of a generalized continued fraction for 4/Pi.
Sequence in context: A124910 A090388 A021370 * A011049 A075639 A082737
Adjacent sequences: A088535 A088536 A088537 * A088539 A088540 A088541
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KEYWORD
| cons,nonn
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AUTHOR
| Benoit Cloitre (benoit7848c(AT)orange.fr), Nov 16 2003
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