A082864 Decimal expansion of (-1)*c(2) 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).

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

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(2) = (EulerGamma^3 - 3*EulerGamma*zeta(2) + zeta(3))/6 = -0.24234545222... ( where EulerGamma is the Euler-Mascheroni constant (A001620)).

Example

0.2423454522273609497622936284606714838388922157911892404874444...

Mathematica

RealDigits[-(EulerGamma^3 - 3*EulerGamma*Zeta[2] + Zeta[3])/6, 10, 100][[1]] (* G. C. Greubel, Sep 05 2018 *)

Prog

(PARI) -(Euler^3-3*Euler*zeta(2)+zeta(3))/6
(Magma) SetDefaultRealField(RealField(100)); L:=RiemannZeta(); R:= RealField(); -(EulerGamma(R)^3 - 3*EulerGamma(R)*Evaluate(L, 2) + Evaluate(L, 3))/6; // G. C. Greubel, Sep 05 2018

Crossrefs

Cf. A013661 (zeta(2)), A002117 (zeta(3)), A001620 (Euler-Mascheroni constant).

Sequence in context: A330312 A331810 A182817 * A134447 A093056 A271320

Adjacent sequences: A082861 A082862 A082863 * A082865 A082866 A082867

Keyword

cons,nonn

Author

Benoit Cloitre, May 24 2003

Status

approved