A070860 Decimal expansion of (-1)*c(1) where, in a neighborhood of zero, Gamma(x) = 1/x + c(0) + c(1)*x + c(2)*x^2 + ... (Gamma(x) denotes the Gamma function).

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

References

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

Links

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

Formula

c(1) = (EulerGamma^2 - zeta(2))/2 = -0.65587807152025388... ( c(0) = -EulerGamma where EulerGamma is the Euler-Mascheroni constant (A001620)).

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: A137727 A010497 A167918 * A198354 A195956 A336814

Adjacent sequences: A070857 A070858 A070859 * A070861 A070862 A070863

Keyword

cons,nonn

Author

Benoit Cloitre, May 24 2003

Status

approved