A291486 Decimal expansion of Gamma''''(1).

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

Offset

2,1

Links

G. C. Greubel, Table of n, a(n) for n = 2..10000

Formula

Equals EulerGamma^4 + EulerGamma^2*Pi^2 + 8*EulerGamma*Zeta(3) + 3*Pi^4/20.

Equals Integral_{x=0..oo} exp(-x)*log(x)^4 dx. - Amiram Eldar, Aug 06 2020

Example

23.56147408402560449607312705652442040865376831336316996971897893425256...

Maple

c:= subs(x=1.0, diff(GAMMA(x), x$4)):
evalf(c, 120);  # Alois P. Heinz, Jul 01 2023

Mathematica

RealDigits[Gamma''''[1], 10, 111][[1]]

Prog

(PARI) default(realprecision, 100); Euler^4 + Euler^2*Pi^2 + 8*Euler*zeta(3) + 3*Pi^4/20 \\ G. C. Greubel, Sep 07 2018
(Magma) SetDefaultRealField(RealField(100)); R:= RealField(); L:=RiemannZeta(); EulerGamma(R)^4 + EulerGamma(R)^2*Pi(R)^2 + 8*EulerGamma(R)*Evaluate(L, 3) + 3*Pi(R)^4/20; // G. C. Greubel, Sep 07 2018

Crossrefs

Cf. A000796 (Pi), A001620 (EulerGamma), A002117 (zeta(3)), A081855, A261509.

Sequence in context: A370730 A157260 A336017 * A177870 A094872 A361443

Adjacent sequences: A291483 A291484 A291485 * A291487 A291488 A291489

Keyword

nonn,cons

Author

Robert G. Wilson v, Aug 24 2017

Status

approved