A098198 - OEIS

%I #26 Mar 18 2023 08:49:14

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

%H 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 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>

%F Decimal expansion of limit of q(n)= A024916(n)/A002088(n) = SummatorySigma / SummatoryTotient.

%F Equals Sum_{n>=1} A000005(n)/n^2. - _R. J. Mathar_, Dec 18 2010

%F Equals 10*Sum_{n>=2} (psi(n)+gamma)/n^3. - _Jean-François Alcover_, Feb 25 2013

%e 2.70580808427784547879000924135291975693687737979... = 2*A152649 = A013661^2.

%t RealDigits[N[Pi^4/36, 256]]

%o (PARI) zeta(2)^2 \\ _Charles R Greathouse IV_, Aug 08 2013

%Y Cf. A002088, A024916.

%K cons,nonn

%O 1,1

%A _Labos Elemer_, Sep 21 2004