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A345203 Decimal expansion of zeta(2) + 2*zeta(3). 1
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 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
Ovidiu Furdui, Limits, Series, and Fractional Part Integrals, Springer, 2013, section 3.71, p. 150.
LINKS
Ovidiu Furdui, Series Involving Products of Two Harmonic Numbers, Mathematics Magazine, Vol. 84, No. 5 (2011), pp. 371-377.
FORMULA
Equals A013661 + 2 * A002117.
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.
EXAMPLE
4.04904787316741500727189148966892517074892248588779...
MATHEMATICA
RealDigits[Zeta[2] + 2*Zeta[3], 10, 100][[1]]
CROSSREFS
Sequence in context: A176714 A055951 A165032 * A088374 A156732 A200341
KEYWORD
nonn,cons
AUTHOR
Amiram Eldar, Jun 10 2021
STATUS
approved

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Last modified March 28 17:25 EDT 2024. Contains 371254 sequences. (Running on oeis4.)