login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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. 9
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 (list; constant; graph; refs; listen; history; text; internal format)
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-Fran├žois Alcover, Jul 16 2014

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified June 24 12:30 EDT 2021. Contains 345416 sequences. (Running on oeis4.)