A245275 - OEIS

%I #10 Feb 16 2025 08:33:23

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

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

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

%N Decimal expansion of sum_{r in Z}(1/r^2) where Z is the set of all nontrivial zeros r of the Riemann zeta function.

%D Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 2.21 Stieltjes Constants, p. 168.

%H Eric Weisstein's MathWorld, <a href="https://mathworld.wolfram.com/StieltjesConstants.html">Stieltjes Constants</a>

%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Stieltjes_constants">Stieltjes constants</a>

%F -Pi^2/8 + gamma^2 + 2*gamma(1) + 1, where gamma is Euler's constant and gamma(1) is the first Stieltjes constant.

%e -0.046154317295804602757107990379077303530267962324144990348848453508...

%t Join[{0}, RealDigits[-Pi^2/8 + EulerGamma^2 + 2*StieltjesGamma[1] + 1, 10, 104] // First]

%o (PARI) -Pi^2/8+Euler^2+1+2*intnum(x=0,oo,(1/tanh(Pi*x)-1)*(x*log(1+x^2)-2*atan(x))/(2*(1+x^2))) \\ _Charles R Greathouse IV_, Mar 10 2016

%Y Cf. A082633, A074760, A195423, A245276.

%K nonn,cons,changed

%O 0,2

%A _Jean-François Alcover_, Jul 16 2014