A245275 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.

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, 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, 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

Offset: 0

Author

Jean-François Alcover, Jul 16 2014

Keywords

• nonn
• cons

Examples

			-0.046154317295804602757107990379077303530267962324144990348848453508...
		

References

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

Links

• Eric Weisstein's MathWorld, Stieltjes Constants
• Wikipedia, Stieltjes constants

Crossrefs

Cf. A082633, A074760, A195423, A245276.

Programs

Mathematica

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

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

Formula

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