A385612 Decimal expansion zeta''''(0) (negated).
2, 3, 9, 9, 7, 1, 0, 3, 1, 8, 8, 0, 1, 3, 7, 0, 7, 9, 5, 8, 9, 8, 7, 2, 1, 9, 5, 2, 7, 7, 4, 1, 0, 0, 5, 6, 6, 1, 8, 9, 1, 1, 3, 9, 9, 3, 4, 9, 2, 1, 7, 0, 3, 4, 2, 4, 9, 7, 6, 0, 0, 9, 3, 3, 3, 0, 4, 6, 3, 8, 2, 9, 3, 8, 6, 3, 3, 4, 4, 9, 9, 1, 3, 8, 2, 8, 6, 1, 8, 2, 2, 7, 5, 7, 8, 1, 3, 3, 4, 6, 9, 4, 9, 0, 3
Offset: 2
Examples
23.997103188013707958987219527741...
Links
- Tom M. Apostol, Formulas for higher derivatives of the Riemann zeta function, Mathematics of Computation 44 (1985), pp. 223-232.
Programs
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Maple
evalf(-Zeta(4, 0), 120); # Vaclav Kotesovec, Jul 04 2025
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Mathematica
RealDigits[-3 EulerGamma^4/2 - EulerGamma^2 Pi^2/4 + 19 Pi^4/480 - 4 EulerGamma^3 Log[2 Pi] - 3 EulerGamma^2 Log[2Pi]^2 + Pi^2 Log[2 Pi]^2/4 + Log[2 Pi]^4/2 - 6 EulerGamma^2 StieltjesGamma[1] - Pi^2 StieltjesGamma[1]/2 - 12 EulerGamma Log[2 Pi] StieltjesGamma[1] - 6 Log[2 Pi]^2 StieltjesGamma[1] - 6 EulerGamma StieltjesGamma[2] - 6 Log[2Pi] StieltjesGamma[2] - 2 StieltjesGamma[3] + 4 Log[2 Pi] Zeta[3],10,105][[1]]
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PARI
-zeta''''(0)
Formula
Equals -3*gamma^4/2 - gamma^2*Pi^2/4 + 19*Pi^4/480 - 4*gamma^3*log(2*Pi) -3*gamma^2*log(2*Pi)^2 + Pi^2*log(2*Pi)^2/4 + log(2*Pi)^4/2 - 6*gamma^2*StieltjesGamma(1) - Pi^2*StieltjesGamma(1)/2 - 12*gamma*log(2*Pi)* StieltjesGamma(1) - 6*log(2*Pi)^2*StieltjesGamma(1) - 6*gamma*StieltjesGamma(2) - 6*log(2*Pi)*StieltjesGamma(2) - 2*StieltjesGamma(3) + 4*log(2*Pi)*zeta(3).
Comments