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A242612
Decimal expansion of the sum of the alternating series tau(4), with tau(n) = Sum_{k>0} (-1)^k*log(k)^n/k.
3
0, 1, 7, 9, 9, 6, 9, 3, 8, 1, 0, 6, 8, 9, 1, 4, 0, 7, 7, 9, 5, 3, 6, 7, 8, 2, 1, 4, 3, 6, 1, 5, 2, 6, 2, 3, 8, 9, 8, 1, 1, 2, 3, 4, 5, 1, 3, 9, 0, 2, 3, 3, 4, 9, 2, 9, 4, 5, 0, 2, 4, 7, 9, 9, 9, 1, 3, 2, 2, 5, 6, 2, 4, 6, 3, 8, 0, 8, 5, 8, 4, 3, 0, 9, 4, 2, 9, 7, 0, 5, 9, 1, 9, 5, 1, 4, 2, 4, 2, 9, 9
OFFSET
0,3
REFERENCES
Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, chapter 2.21, p. 168.
LINKS
FORMULA
tau(n) = -log(2)^(n+1)/(n+1) + Sum_(k=0..n-1) (binomial(n, k)*log(2)^(n-k)*gamma(k)).
tau(4) = gamma*log(2)^4 - (1/5)*log(2)^5 + 4*log(2)^3*gamma(1) + 6*log(2)^2*gamma(2) + 4*log(2)*gamma(3).
EXAMPLE
-0.017996938106891407795367821436152623898...
MATHEMATICA
tau[n_] := -Log[2]^(n+1)/(n+1) + Sum[Binomial[n, k]*Log[2]^(n-k)*StieltjesGamma[k], {k, 0, n-1}]; Join[{0}, RealDigits[tau[4], 10, 100] // First]
PROG
(PARI) sumalt(k=1, (-1)^k*log(k)^4/k) \\ Charles R Greathouse IV, Mar 10 2016
KEYWORD
nonn,cons
AUTHOR
STATUS
approved