A195055 Decimal expansion of Pi^2/3.

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

Offset

1,1

References

Marc Briane and Gilles Pagès, Théorie de l'Intégration, Vuibert, 2004, 3ème édition, exercice 12.15, p. 256.

Links

Table of n, a(n) for n=1..105.

George E. Andrews, Partitions with short sequences and mock theta functions, Proceedings of the National Academy of Sciences, Vol. 102, No. 13 (2005), pp. 4666-4671.

Index entries for transcendental numbers

Formula

Equals 3 + A145426.

Equals -Sum_{n>=1} Psi_2(n), where Psi_2 is the tetragamma function. - Istvan Mezo, Oct 25 2012

Equals Integral_{x=0..1} (log(x)/(x - 1))^2 dx. - Jean-François Alcover, Mar 21 2013

Equals Integral_{x=-oo..oo} x^2/sinh(x)^2 dx. - Amiram Eldar, Aug 06 2020

Equals Integral_{x=0..oo} (log(x+1)/x)^2 dx (reference Briane and Pagès). - Bernard Schott, Feb 13 2022

Example

3.289868133696452872944830333292050378438...

Mathematica

RealDigits[Pi^2/3, 10, 105][[1]] (* T. D. Noe, Oct 05 2011 *)

Prog

(Magma) pi:=Pi(RealField(110)); Reverse(Intseq(Floor(10^105*pi^2/3))); // Vincenzo Librandi, Jan 12 2016
(PARI) 2*zeta(2) \\ Charles R Greathouse IV, Jan 20 2022
(PARI) sumnumrat(1/x^2, -oo) \\ Charles R Greathouse IV, Jan 20 2022

Crossrefs

Cf. A002388, A102753, A091476, 2*A013661, A164102.

Cf. A024916 (partial sums of A000203).

Sequence in context: A328645 A021308 A274181 * A214683 A363816 A060921

Adjacent sequences: A195052 A195053 A195054 * A195056 A195057 A195058

Keyword

nonn,cons

Author

Omar E. Pol, Oct 04 2011

Extensions

Extended by T. D. Noe, Oct 05 2011

Status

approved