A384462 Decimal expansion of Sum_{k>=1} H(k)^3/k^3, where H(k) = A001008(k)/A002805(k) is the k-th harmonic number.
2, 3, 0, 0, 9, 5, 4, 5, 5, 1, 7, 0, 0, 5, 2, 5, 0, 3, 9, 8, 0, 6, 4, 2, 2, 7, 6, 9, 8, 9, 2, 2, 5, 6, 0, 0, 0, 4, 6, 9, 9, 7, 5, 6, 4, 6, 4, 0, 6, 2, 3, 9, 6, 4, 2, 8, 8, 0, 4, 1, 4, 9, 5, 4, 7, 7, 8, 7, 2, 1, 1, 7, 2, 7, 8, 9, 2, 4, 5, 0, 2, 6, 5, 2, 8, 1, 4, 1, 0, 0, 0, 4, 7, 1, 4, 4, 1, 9, 7, 7, 0, 5, 7, 4, 1
Offset: 1
Examples
2.30095455170052503980642276989225600046997564640623...
References
- Ali Shadhar Olaikhan, An Introduction to the Harmonic Series and Logarithmic Integrals, 2021, p. 231, eq. (4.126).
Links
- Cornel Ioan Vălean, A master theorem of series and an evaluation of a cubic harmonic series, Journal of Classical Analysis, Vol. 10, No. 2 (2017), pp. 97-107.
- Cornel Ioan Vălean, (Almost) Impossible Integrals, Sums, and Series, Springer International Publishing, 2019, p. 294, eq. (4.35).
Crossrefs
Programs
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Mathematica
RealDigits[93*Zeta[6]/16 - 5*Zeta[3]^2/2, 10, 120][[1]]
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PARI
93*zeta(6)/16 - 5*zeta(3)^2/2
Formula
Equals 93*zeta(6)/16 - 5*zeta(3)^2/2.