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%I #15 May 06 2023 04:16:25
%S 7,5,1,2,8,5,5,6,4,4,7,4,7,4,6,4,2,8,3,7,4,8,3,6,3,5,0,9,4,4,6,5,6,2,
%T 4,4,2,2,8,1,1,6,4,3,2,7,1,2,8,1,1,8,0,1,1,2,0,1,6,9,7,2,2,0,8,8,6,4,
%U 8,8,7,8,6,1,6,4,4,5,6,8,1,3,6,6,5,3,4,9,2,1,0,0,5,8,3,4,5,3,6,3
%N Decimal expansion of Sum_{n>=1} (-1)^(n-1)*H(n)/n^2, where H(n) is the n-th harmonic number.
%H Philippe Flajolet and Bruno Salvy, <a href="http://algo.inria.fr/flajolet/Publications/FlSa98.pdf">Euler Sums and Contour Integral Representations</a>, Experimental Mathematics 7:1 (1998), page 32.
%F Equals 5*zeta(3)/8.
%F Equals -Integral_{x=0..1} (log(1+x)*log(1-x)/x)*dx. - _Amiram Eldar_, May 06 2023
%e 0.7512855644747464283748363509446562442281164327128118011201697220886...
%t RealDigits[ 5*Zeta[3]/8, 10, 100] // First
%Y Cf. A002117 (zeta(3)), A197070 (3*zeta(3)/4), A233091 (7*zeta(3)/8), A076788 (alternating sum with denominator n), A152648 (non-alternating sum with denominator n^2), A152649 (non-alternating sum with denominator n^3), A233033 (alternating sum with denominator n^3).
%K nonn,cons
%O 0,1
%A _Jean-François Alcover_, Dec 04 2013, after the comment by _Peter Bala_ about A233033.
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