OFFSET
1,2
COMMENTS
Also the decimal expansion of the Integral_{x>=0} exp(-x)*(log(x))^2 dx. - Robert G. Wilson v, Aug 18 2017
REFERENCES
Bruce C. Berndt, Ramanujan's notebooks Part II, Springer, p. 179
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.
FORMULA
The second derivative of Gamma(x) at x=1 is Gamma^2+zeta(2) = 1.97811199... where Gamma is the Euler constant and zeta(2) = Pi^2/6.
EXAMPLE
1.978111990655945110790791303001269415878367... [corrected by Georg Fischer, Jul 29 2021]
MATHEMATICA
EulerGamma^2 + Zeta[2] // RealDigits[#, 10, 105] & // First (* Jean-François Alcover, Apr 29 2013 *)
RealDigits[ Integrate[ Exp[-x]*Log[x]^2, {x, 0, Infinity}], 10, 111][[1]] (* Robert G. Wilson v, Aug 18 2017 *)
PROG
(PARI) Euler^2+zeta(2) \\ Charles R Greathouse IV, Aug 18 2017
(PARI) intnum(x=0, [oo, 1], exp(-x)*log(x)^2) \\ Charles R Greathouse IV, Aug 18 2017
(Magma) SetDefaultRealField(RealField(100)); R:= RealField(); L:=RiemannZeta(); EulerGamma(R)^2 + Evaluate(L, 2); // G. C. Greubel, Aug 29 2018
CROSSREFS
KEYWORD
cons,nonn
AUTHOR
Benoit Cloitre, Apr 11 2003
STATUS
approved