cp's OEIS Frontend

A098198 Decimal expansion of Pi^4/36 = zeta(2)^2.

%I A098198 #35 Aug 08 2025 09:10:42
%S A098198 2,7,0,5,8,0,8,0,8,4,2,7,7,8,4,5,4,7,8,7,9,0,0,0,9,2,4,1,3,5,2,9,1,9,
%T A098198 7,5,6,9,3,6,8,7,7,3,7,9,7,9,6,8,1,7,2,6,9,2,0,7,4,4,0,5,3,8,6,1,0,3,
%U A098198 0,1,5,4,0,4,6,7,4,2,2,1,1,6,3,9,2,2,7,4,0,8,9,8,5,4,2,4,9,7,9,3,0,8,2,4,7
%N A098198 Decimal expansion of Pi^4/36 = zeta(2)^2.
%H A098198 Ce Xu and Jianqiang Zhao, <a href="https://arxiv.org/abs/2203.04184">Sun's Three Conjectures on Apéry-like Sums Involving Harmonic Numbers</a>, arXiv:2203.04184 [math.NT], 2022.
%H A098198 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>
%F A098198 Decimal expansion of limit of q(n)= A024916(n)/A002088(n) = SummatorySigma / SummatoryTotient.
%F A098198 Equals Sum_{n>=1} A000005(n)/n^2. - _R. J. Mathar_, Dec 18 2010
%F A098198 Equals 10*Sum_{n>=2} (psi(n)+gamma)/n^3. - _Jean-François Alcover_, Feb 25 2013
%F A098198 Equals Zeta(4)*10/4 = A013662/0.4 = 1/A227929. - _R. J. Mathar_, Jul 20 2025
%F A098198 Equals 10 * zeta(3,1) = 10 * Sum_{n >= 1} 1/n Sum_{k >= n+1} 1/k^3 = 10 * Sum_{n >= 1} 1/n^3 * Sum_{k = 1..n-1} 1/k. - _Peter Bala_, Aug 07 2025
%e A098198 2.70580808427784547879000924135291975693687737979... = 2*A152649 = A013661^2.
%t A098198 RealDigits[N[Pi^4/36, 256]]
%o A098198 (PARI) zeta(2)^2 \\ _Charles R Greathouse IV_, Aug 08 2013
%Y A098198 Cf. A002088, A024916.
%K A098198 cons,nonn
%O A098198 1,1
%A A098198 _Labos Elemer_, Sep 21 2004