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A245058
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Decimal expansion of the real part of Li_2(I), negated.
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12
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2, 0, 5, 6, 1, 6, 7, 5, 8, 3, 5, 6, 0, 2, 8, 3, 0, 4, 5, 5, 9, 0, 5, 1, 8, 9, 5, 8, 3, 0, 7, 5, 3, 1, 4, 8, 6, 5, 2, 3, 6, 8, 7, 3, 7, 6, 5, 0, 8, 4, 9, 8, 0, 4, 7, 1, 6, 9, 4, 4, 7, 7, 8, 6, 7, 1, 2, 5, 0, 9, 3, 3, 8, 0, 0, 4, 0, 0, 1, 0, 9, 2, 2, 9, 2, 0, 3, 6, 1, 2, 5, 7, 7, 4, 6, 9, 8, 3, 8, 1, 6, 3, 0, 0, 0
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OFFSET
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0,1
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COMMENTS
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This is the decimal expansion of the real part of the dilogarithm of the square root of -1. The imaginary part is Catalan's number (A006752).
5*Pi^2/24 = 10 * (this constant) equals the asymptotic mean of the abundancy index of the even numbers. - Amiram Eldar, May 12 2023
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LINKS
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FORMULA
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Also equals -zeta(2)/8 = -Pi^2/48.
Also equals the Bessel moment Integral_{0..inf} x I_1(x) K_0(x)^2 K_1(x) dx. - Jean-François Alcover, Jun 05 2016
Equals Sum_{n>=0} (-1)^n/(2n+2)^2.
Equals (Sum_{n>=1} 1/(2n)^2)/2 = A222171/2. (End)
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EXAMPLE
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0.2056167583560283045590518958307531486523687376508498047169447786712509338004...
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MATHEMATICA
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RealDigits[ Re[ PolyLog[2, I]], 10, 111][[1]] (* or *) RealDigits[ Zeta[2]/8, 10, 111][[1]] (* or *) RealDigits[ Pi^2/48, 10, 111][[1]]
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PROG
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(Sage)
(Magma) SetDefaultRealField(RealField(100)); R:=RealField(); Pi(R)^2/48; // G. C. Greubel, Aug 25 2018
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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