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A086054
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Decimal expansion of Pi*log(2).
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8
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2, 1, 7, 7, 5, 8, 6, 0, 9, 0, 3, 0, 3, 6, 0, 2, 1, 3, 0, 5, 0, 0, 6, 8, 8, 8, 9, 8, 2, 3, 7, 6, 1, 3, 9, 4, 7, 3, 3, 8, 5, 8, 3, 7, 0, 0, 3, 6, 9, 2, 8, 6, 2, 9, 4, 3, 2, 5, 7, 9, 5, 2, 5, 3, 1, 9, 4, 3, 0, 8, 5, 4, 9, 1, 7, 6, 7, 4, 1, 9, 8, 6, 4, 3, 0, 3, 2, 8, 9, 6, 1, 6, 1, 0, 6, 6, 3, 0, 2, 5, 0, 5, 7, 6, 1
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OFFSET
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1,1
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COMMENTS
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Madelung constant b2(2), negated.
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REFERENCES
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G. Boros and V. H. Moll, Irresistible Integrals: Symbolics, Analysis and Experiments in the Evaluation of Integrals, Cambridge University Press, 2004 (equation 13.6.6).
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LINKS
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FORMULA
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Pi*log(2) = -(8/3)*int(log(x)/sqrt(1+4*x-4*x^2), x=0..1). - John M. Campbell, Feb 07 2012
Pi*log(2) = int((x/sin(x))^2, x=0..Pi/2) = int(log(x^2+1)/(x^2+1), x=0..infinity) = int(-log(cos(x)), x=-Pi/2..Pi/2) = int(arctan(1/x)^2, x=0..infinity). - Jean-François Alcover, May 30 2013
Equals Integral_{x=-1..1} arcsin(x) dx / x.
Equals Integral_{x=-Pi/2..Pi/2} x*cot(x) dx. (End)
Equals Integral_{x = 0..oo} log(x^2 + 4)/(x^2 + 4) dx. - Peter Bala, Jul 22 2022
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EXAMPLE
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2.1775860903036021305006888982376139...
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MATHEMATICA
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CROSSREFS
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KEYWORD
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AUTHOR
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EXTENSIONS
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Corrected by Antti Ahti (antti.ahti(AT)tkk.fi), Nov 17 2004
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STATUS
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approved
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