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Search: id:A094640
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| A094640 |
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Decimal expansion of log 4/Pi. |
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+0
8
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| 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, 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, 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
(list; cons; graph; listen)
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OFFSET
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0,1
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COMMENT
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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
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REFERENCES
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G. Boros and V. Moll, Irresistible Integrals: Symbolics, Analysis and Experiments in the Evaluation of Integrals, Cambridge University Press, Cambridge, 2004, Chap. 7.
J. Borwein and P. Borwein, Pi and the AGM, John Wiley & Sons, New York, 1987, Chap. 11.
D. Huylebrouck, Similarities in irrationality proofs for Pi, ln2, zeta(2) and zeta(3), Amer. Math. Monthly 108 (2001) 222-231.
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.
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LINKS
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J. Sondow, Double Integrals for Euler's Constant and ln(4/Pi).
Eric Weisstein's World of Mathematics, Euler-Mascheroni Constant
Eric Weisstein's World of Mathematics, Hadjicostas's Formula
J. Sondow, New Vacca-Type Rational Series for Euler's Constant and Its "Alternating" Analog ln(4/Pi)
Eric Weisstein's World of Mathematics, Digit Count
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EXAMPLE
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log(4/Pi) = 0.24156447527...
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MATHEMATICA
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RealDigits[ Log[4/Pi], 10, 111][[1]]
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CROSSREFS
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Cf. A094641. See also A103130.
Cf. A110625, A110626.
Sequence in context: A060370 A165064 A021418 this_sequence A070937 A059573 A080427
Adjacent sequences: A094637 A094638 A094639 this_sequence A094641 A094642 A094643
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KEYWORD
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cons,easy,nonn
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AUTHOR
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Jonathan Sondow (jsondow(AT)alumni.princeton.edu) and Robert G. Wilson v (rgwv(AT)rgwv.com), May 18 2004
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