A070860 Decimal expansion of Pi^2/12 - gamma^2 /2.

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

Offset

0,1

Comments

This is erroneously computed as the linear term in the Laurent expansion of Gamma(x) = 1/x +c(0) + c(1)*x+ O(x^2) on page 135 of the Patterson book. The correct value of c(1) is A090998. - R. J. Mathar, Jul 11 2025

Links

G. C. Greubel, Table of n, a(n) for n = 0..10000

R. J. Mathar, Erratum to Exercise A4.2 in "An Introduction to the Theory of the Riemann Zeta Function", viXra:2507.0094 (2025)

S. J. Patterson, An introduction to the theory of the Riemann zeta function, Cambridge studies in advanced mathematics no. 14, (1988) p. 135

Formula

(EulerGamma^2 - zeta(2))/2 = -0.65587807152025388....

Equals A072691 - A155969/2.

Example

0.65587807152025388107701951514539048127976638047858434729236244568387...

Mathematica

RealDigits[(Zeta[2] - EulerGamma^2)/2, 10, 100][[1]] (* G. C. Greubel, Sep 05 2018 *)

Prog

(PARI) -(Euler^2-zeta(2))/2
(Magma) R:= RealField(100); (Pi(R)^2 - 6*EulerGamma(R)^2)/12; // G. C. Greubel, Sep 05 2018

Crossrefs

Sequence in context: A010497 A392406 A167918 * A198354 A195956 A336814

Adjacent sequences: A070857 A070858 A070859 * A070861 A070862 A070863

Keyword

cons,nonn

Author

Benoit Cloitre, May 24 2003

Status

approved