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

0,2

References

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

Links

Table of n, a(n) for n=0..104.

Eric Weisstein's MathWorld, Stieltjes Constants

Wikipedia, Stieltjes constants

Formula

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

Example

-0.046154317295804602757107990379077303530267962324144990348848453508...

Mathematica

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

Prog

(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

Crossrefs

Cf. A082633, A074760, A195423, A245276.

Sequence in context: A309445 A051261 A247621 * A030169 A263180 A239809

Adjacent sequences: A245272 A245273 A245274 * A245276 A245277 A245278

Keyword

nonn,cons

Author

Jean-François Alcover, Jul 16 2014

Status

approved