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A345203
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Decimal expansion of zeta(2) + 2*zeta(3).
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1
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4, 0, 4, 9, 0, 4, 7, 8, 7, 3, 1, 6, 7, 4, 1, 5, 0, 0, 7, 2, 7, 1, 8, 9, 1, 4, 8, 9, 6, 6, 8, 9, 2, 5, 1, 7, 0, 7, 4, 8, 9, 2, 2, 4, 8, 5, 8, 8, 7, 7, 9, 6, 2, 0, 1, 3, 2, 0, 1, 0, 1, 3, 4, 0, 0, 5, 3, 6, 8, 3, 8, 8, 1, 9, 7, 5, 8, 2, 7, 0, 5, 4, 2, 0, 6, 5, 4
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OFFSET
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1,1
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COMMENTS
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Ovidiu Furdui, Limits, Series, and Fractional Part Integrals, Springer, 2013, section 3.71, p. 150.
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LINKS
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FORMULA
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Equals Sum_{k>=1} (k+2)/k^3.
Equals Sum_{k>=1} H(k)*H(k+1)/(k*(k+1)), where H(k) = A001008(k)/A002805(k) is the k-th harmonic number (Furdui, 2011).
Equals Sum_{k>=1} (H(k)+1)/k^2.
Equals 1 + Sum_{k>=2} H(k)/(k-1)^2.
Equals Sum_{k>=2} (k-1)^2*(zeta(k)-1).
Equals 3 + Sum_{k>=3} (-1)^(k+1)*k^2*(zeta(k)-1).
Equals Integral_{x=0..1} log(x)*(log(x)-1)/(1-x) dx.
Equals Integral_{x>=1} log(x)*(log(x)+1)/(x*(x-1)) dx.
Equals Integral_{x>=0} x*(x+1)/(exp(x)-1) dx.
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EXAMPLE
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4.04904787316741500727189148966892517074892248588779...
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MATHEMATICA
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RealDigits[Zeta[2] + 2*Zeta[3], 10, 100][[1]]
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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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