A304658 - OEIS

%I #17 Sep 07 2018 20:31:26

%S 7,3,5,4,6,7,0,6,2,6,0,1,2,2,4,1,4,5,9,3,3,0,7,2,6,3,3,0,9,6,4,8,4,7,

%T 7,3,7,7,4,3,7,6,9,7,0,6,8,6,3,8,8,0,4,5,5,3,7,3,9,3,9,3,0,8,9,2,3,2,

%U 2,2,0,6,8,9,3,0,0,3,2,0,3,9,3,1,7,1,2

%N Decimal expansion of (1/6)*(3*gamma(0)^2 + Pi^2)*(gamma(0)^2 - gamma(1)) where gamma(n) are the generalized Stieltjes constants.

%C Consider the Laurent expansion of Gamma(s)Zeta(s) = (s-1)^(-1) + Sum_{n>=0} c(n) (s-1)^n. c(0) is Euler's gamma and -c(1) is this constant.

%H G. C. Greubel, <a href="/A304658/b304658.txt">Table of n, a(n) for n = 0..10000</a>

%H Tom M. Apostol, <a href="https://doi.org/10.1090/S0025-5718-1985-0771044-5">Formulas for higher derivatives of the Riemann zeta function</a>, Mathematics of Computation 44 (1985), p. 223-232.

%e Equals 0.7354670626012241459330726330964847737743769706863880...

%t RealDigits[(1/6)*(3*EulerGamma^2 + Pi^2)*(EulerGamma^2 - StieltjesGamma[1]), 10, 100][[1]] (* modified by _G. C. Greubel_, Sep 07 2018 *)

%Y Cf. A001620.

%K nonn,cons

%O 0,1

%A _Peter Luschny_, May 16 2018