A397199 - OEIS

%I #4 Jun 18 2026 00:46:10

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

%T 5,2,0,1,3,3,6,9,8,1,8,8,9,6,1,8,5,3,6,5,8,3,8,2,9,6,5,0,7,3,2,9,3,8,

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

%N Decimal expansion of Sum_{k>=1} AH(k)/k^2, where AH(k) = A058313(k)/A058312(k) is the k-th alternating harmonic (or skew-harmonic) number.

%H Cornel Ioan Vălean, <a href="https://doi.org/10.1007/978-3-031-21262-8">More (Almost) Impossible Integrals, Sums, and Series</a>, Springer Cham, 2023. See section 4.22, p. 425.

%H <a href="/index/Ha#harmonic">Index entries for sequences related to harmonic numbers</a>.

%F Equals 3*log(2)*zeta(2)/2 - zeta(3)/4.

%e 1.409757890174380564861935248110661520133698188961853...

%t RealDigits[3*Log[2]*Zeta[2]/2 - Zeta[3]/4, 10, 120][[1]]

%o (PARI) 3*log(2)*zeta(2)/2 - zeta(3)/4

%Y Cf. A058312, A058313.

%Y Cf. A002117, A002162, A013661.

%Y Sum_{k>=1} AH(k)/k^m: this constant (m=2), A397200 (m=3), A397201 (m=4).

%K nonn,cons

%O 1,2

%A _Amiram Eldar_, Jun 18 2026