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
Examples
23.56147408402560449607312705652442040865376831336316996971897893425256...
Links
- G. C. Greubel, Table of n, a(n) for n = 2..10000
Programs
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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
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Maple
c:= subs(x=1.0, diff(GAMMA(x), x$4)): evalf(c, 120); # Alois P. Heinz, Jul 01 2023
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Mathematica
RealDigits[Gamma''''[1], 10, 111][[1]]
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PARI
default(realprecision, 100); Euler^4 + Euler^2*Pi^2 + 8*Euler*zeta(3) + 3*Pi^4/20 \\ G. C. Greubel, Sep 07 2018
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