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
Examples
3.289868133696452872944830333292050378438...
References
- Marc Briane and Gilles Pagès, Théorie de l'Intégration, Vuibert, 2004, 3ème édition, exercice 12.15, p. 256.
Links
- 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
Crossrefs
Programs
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Magma
pi:=Pi(RealField(110)); Reverse(Intseq(Floor(10^105*pi^2/3))); // Vincenzo Librandi, Jan 12 2016
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Mathematica
RealDigits[Pi^2/3, 10, 105][[1]] (* T. D. Noe, Oct 05 2011 *)
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PARI
2*zeta(2) \\ Charles R Greathouse IV, Jan 20 2022
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PARI
sumnumrat(1/x^2,-oo) \\ Charles R Greathouse IV, Jan 20 2022
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
Equals Sum_{n>=1} H(n) * binomial(2*n, n) / (n * 4^n), where H(n) is the n-th harmonic number. - Antonio Graciá Llorente, Apr 04 2025
Extensions
Extended by T. D. Noe, Oct 05 2011