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

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, 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, 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

Offset: 1

Author

Labos Elemer, Sep 21 2004

Keywords

• cons
• nonn

Examples

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

Links

• Ce Xu and Jianqiang Zhao, Sun's Three Conjectures on Apéry-like Sums Involving Harmonic Numbers, arXiv:2203.04184 [math.NT], 2022.
• Index entries for transcendental numbers

Crossrefs

Cf. A002088, A024916.

Programs

Mathematica

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

PARI

zeta(2)^2 \\ Charles R Greathouse IV, Aug 08 2013

Formula

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

Equals Sum_{n>=1} A000005(n)/n^2. - R. J. Mathar, Dec 18 2010

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

Equals Zeta(4)*10/4 = A013662/0.4 = 1/A227929. - R. J. Mathar, Jul 20 2025

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