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A349220 Decimal expansion of Sum_{k>=1} (-1)^k * log(k) / k^3. 1
0, 5, 9, 7, 0, 5, 9, 0, 6, 1, 6, 0, 1, 9, 5, 3, 5, 8, 3, 6, 3, 4, 2, 9, 2, 6, 6, 2, 8, 7, 9, 2, 5, 6, 7, 8, 3, 1, 6, 9, 2, 6, 8, 7, 3, 1, 5, 6, 5, 1, 5, 9, 6, 9, 2, 3, 3, 2, 5, 1, 1, 7, 8, 0, 5, 2, 4, 0, 1, 0, 0, 5, 6, 0, 1, 1, 6, 2, 2, 8, 0, 2, 3, 4, 6, 3, 7, 0, 2, 4, 9, 7, 1, 6, 9, 2, 8, 9, 5, 1, 8, 7, 0, 8, 3, 1, 8, 1, 9, 6, 7, 0, 1, 0, 8, 2, 1, 6, 1, 1, 2 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET
0,2
COMMENTS
First derivative of the Dirichlet eta function at 3.
LINKS
Eric Weisstein's World of Mathematics, Dirichlet Eta Function
FORMULA
Equals (log(2) * zeta(3) + 3 * zeta'(3)) / 4.
EXAMPLE
0.0597059061601953583634292662879256783169268731565...
MATHEMATICA
Flatten[{0, RealDigits[(Log[2] Zeta[3] + 3 Zeta'[3])/4, 10, 120][[1]]}]
PROG
(PARI) sumalt(k=1, (-1)^k * log(k) / k^3) \\ Michel Marcus, Nov 11 2021
CROSSREFS
Sequence in context: A176110 A262974 A319757 * A240723 A254154 A121060
KEYWORD
nonn,cons
AUTHOR
Ilya Gutkovskiy, Nov 11 2021
STATUS
approved

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Last modified August 11 01:05 EDT 2024. Contains 375059 sequences. (Running on oeis4.)