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A256576
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Decimal expansion of Ramanujan's constant G(1) = Sum_{r>=1} 1/(2r^3)*(1 + 1/3 + ... + 1/(2r-1)).
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0
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1, 6, 2, 2, 7, 1, 9, 3, 9, 4, 7, 1, 4, 8, 3, 3, 9, 0, 7, 1, 5, 3, 5, 9, 5, 5, 1, 8, 0, 8, 0, 7, 1, 2, 0, 6, 4, 7, 3, 4, 9, 9, 7, 5, 1, 4, 0, 0, 3, 4, 6, 3, 1, 4, 2, 5, 8, 8, 6, 7, 2, 7, 2, 9, 3, 7, 8, 1, 1, 7, 2, 1, 2, 1, 0, 5, 0, 3, 9, 7, 1, 4, 2, 5, 2, 4, 0, 5, 3, 8, 0, 7, 9, 6, 7, 4, 9, 8, 9, 2
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OFFSET
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0,2
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LINKS
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FORMULA
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G(1) = Pi^4/480 - (1/4)*Sum_{r>=2} (-1)^r*H(r-1,2)/r^2, where H(n,m) is the n-th harmonic number of order m.
F(1) = 7*Zeta(3)/16 = Sum_{r>=1} (1+1/3+1/5+..+1/(2r-1))/r^2 = 0.525899895... [Coppo] - R. J. Mathar, Jun 13 2024
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EXAMPLE
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0.1622719394714833907153595518080712064734997514...
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MATHEMATICA
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digits = 100; G1 = NSum[(1/(2*r)^3)*(1/2*(EulerGamma + Log[4]) + 1/2*PolyGamma[ 1/2+r]), {r, 1, Infinity}, WorkingPrecision -> digits+10, NSumTerms -> 40, Method -> {"NIntegrate", "MaxRecursion" -> 10}]; RealDigits[G1, 10, digits] // First
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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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