A242613 -id:A242613 - cp's OEIS frontend

A242611 Decimal expansion of the sum of the alternating series tau(3), with tau(n) = Sum_{k>0} (-1)^k*log(k)^n/k.

0, 0, 9, 4, 1, 3, 9, 5, 0, 2, 3, 2, 4, 9, 3, 0, 8, 9, 7, 3, 5, 1, 7, 1, 9, 5, 5, 3, 6, 2, 3, 3, 3, 0, 2, 8, 9, 8, 1, 5, 8, 3, 1, 7, 3, 7, 9, 6, 6, 5, 4, 3, 0, 0, 3, 7, 1, 1, 4, 2, 3, 4, 0, 2, 8, 0, 2, 1, 6, 1, 8, 7, 3, 0, 0, 0, 8, 4, 5, 1, 3, 3, 5, 8, 7, 3, 0, 9, 0, 6, 2, 2, 8, 1, 1, 7, 2, 7, 5, 4, 5, 4

Offset: 0

Jean-François Alcover, May 19 2014

			0.009413950232493089735171955362333...

Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, chapter 2.21, p. 168.

G. C. Greubel, Table of n, a(n) for n = 0..10000

Cf. A001620, A082633, A086279, A242494, A242612, A242613.

tau[n_] := -Log[2]^(n+1)/(n+1) + Sum[Binomial[n, k]*Log[2]^(n-k)*StieltjesGamma[k], {k, 0, n-1}]; Join[{0,0},RealDigits[tau[3], 10, 100] // First]

-suminf(k=1,(-1)^k*log(k)^n/k) \\ Charles R Greathouse IV, Mar 10 2016

tau(n) = -log(2)^(n+1)/(n+1) + Sum_(k=0..n-1) (binomial(n, k)*log(2)^(n-k)*gamma(k)).

tau(3) = gamma*log(2)^3 - (1/4)*log(2)^4 + 3*log(2)^2*gamma(1) + 3*log(2)*gamma(2).

A242612 Decimal expansion of the sum of the alternating series tau(4), with tau(n) = Sum_{k>0} (-1)^k*log(k)^n/k.

Original entry on oeis.org

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

Jean-François Alcover, May 19 2014

			-0.017996938106891407795367821436152623898...

Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, chapter 2.21, p. 168.

G. C. Greubel, Table of n, a(n) for n = 0..10000

Cf. A001620, A082633, A086279, A086280, A242494, A242611, A242613.

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]

sumalt(k=1,(-1)^k*log(k)^4/k) \\ Charles R Greathouse IV, Mar 10 2016

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).

cp's OEIS Frontend

A242611 Decimal expansion of the sum of the alternating series tau(3), with tau(n) = Sum_{k>0} (-1)^k*log(k)^n/k.

Views

Author

Keywords

Examples

References

Links

Crossrefs

Programs

Mathematica

PARI

Formula