A261509 Decimal expansion of -Gamma'''(1).

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

Offset

1,1

Links

G. C. Greubel, Table of n, a(n) for n = 1..10000

Tom M. Apostol, Formulas for higher derivatives of the Riemann zeta function, Mathematics of Computation 44 (1985), p. 223-232.

Eric Weisstein's World of Mathematics, Gamma Function.

Wikipedia, Gamma function.

Formula

From Amiram Eldar, Aug 06 2020: (Start)

Equals gamma^3 + gamma*Pi^2/2 + 2*zeta(3).

Equals -Integral_{x=0..oo} exp(-x)*log(x)^3 dx. (End)

Example

5.4448744564853177340993610041376506895716686944353825656479...

Mathematica

RealDigits[EulerGamma^3 + (EulerGamma*Pi^2)/2 + 2*Zeta[3], 10, 120][[1]]

Prog

(PARI) default(realprecision, 100); Euler^3 + Euler*Pi^2/2 + 2*zeta(3) \\ G. C. Greubel, Aug 30 2018
(Magma) SetDefaultRealField(RealField(100)); R:= RealField(); L:=RiemannZeta(); EulerGamma(R)^3 + (EulerGamma(R)*Pi(R)^2)/2 + 2*Evaluate(L, 3); // G. C. Greubel, Aug 30 2018

Crossrefs

Cf. A001620, A081855, A002117.

Sequence in context: A243380 A244999 A201129 * A226578 A134206 A134209

Adjacent sequences: A261506 A261507 A261508 * A261510 A261511 A261512

Keyword

nonn,cons

Author

Vaclav Kotesovec, Aug 22 2015

Status

approved