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A247318
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Decimal expansion of p_2, a probability associated with continuant polynomials.
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1
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0, 4, 8, 4, 8, 0, 8, 0, 1, 4, 4, 9, 4, 6, 3, 6, 3, 2, 7, 0, 5, 7, 2, 4, 9, 3, 3, 8, 8, 2, 4, 7, 6, 5, 5, 6, 3, 3, 3, 0, 5, 6, 0, 0, 6, 6, 9, 5, 2, 3, 7, 1, 3, 9, 7, 7, 1, 6, 6, 5, 5, 9, 9, 8, 3, 8, 6, 6, 2, 0, 4, 8, 2, 0, 5, 4, 0, 2, 2, 5, 4, 2, 7, 6, 2, 5, 8, 8, 8, 8, 8, 7, 3, 1, 1, 3, 3, 9, 2, 4, 7, 7
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OFFSET
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0,2
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REFERENCES
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Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 2.19 Vallée's Constant, p. 161.
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LINKS
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FORMULA
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p_2 = sum_{i >= 1}(sum_{j >= 1} 1/((i*j + 1)^2*(i*j + i + 1)^2)).
p_2 = sum_{n >= 0} (-1)^n*(n + 1)*zeta(n + 4)*(zeta(n + 2) - 1).
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EXAMPLE
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0.04848080144946363270572493388247655633305600669523713977...
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MATHEMATICA
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digits = 101; s = NSum[(-1)^n*(n + 1)*Zeta[n + 4]*(Zeta[n + 2] - 1), {n, 0, Infinity}, Method -> "AlternatingSigns", WorkingPrecision -> digits + 10]; p2 = -5 + 2*Pi^2/3 - 2*Zeta[3] + 2*s; Join[{0}, RealDigits[p2, 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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