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
KEYWORD
nonn,cons
AUTHOR
Vaclav Kotesovec, Aug 22 2015
STATUS
approved