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

%I A291486 #25 Jul 01 2023 14:02:04
%S A291486 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,
%T A291486 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,
%U A291486 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
%N A291486 Decimal expansion of Gamma''''(1).
%H A291486 G. C. Greubel, <a href="/A291486/b291486.txt">Table of n, a(n) for n = 2..10000</a>
%F A291486 Equals EulerGamma^4 + EulerGamma^2*Pi^2 + 8*EulerGamma*Zeta(3) + 3*Pi^4/20.
%F A291486 Equals Integral_{x=0..oo} exp(-x)*log(x)^4 dx. - _Amiram Eldar_, Aug 06 2020
%e A291486 23.56147408402560449607312705652442040865376831336316996971897893425256...
%p A291486 c:= subs(x=1.0, diff(GAMMA(x), x$4)):
%p A291486 evalf(c, 120);  # _Alois P. Heinz_, Jul 01 2023
%t A291486 RealDigits[Gamma''''[1], 10, 111][[1]]
%o A291486 (PARI) default(realprecision, 100); Euler^4 + Euler^2*Pi^2 + 8*Euler*zeta(3) + 3*Pi^4/20 \\ _G. C. Greubel_, Sep 07 2018
%o A291486 (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
%Y A291486 Cf. A000796 (Pi), A001620 (EulerGamma), A002117 (zeta(3)), A081855, A261509.
%K A291486 nonn,cons
%O A291486 2,1
%A A291486 _Robert G. Wilson v_, Aug 24 2017