A114721 Denominator of expansion of RiemannSiegelTheta(t) about infinity.

48, 5760, 80640, 430080, 1216512, 1476034560, 2555904, 8021606400, 64012419072, 131491430400, 3472883712, 25282593423360, 20132659200, 25222195445760, 2675794690179072, 2172909854392320, 6803228196864

Offset

1,1

References

H. M. Edwards, Riemann's Zeta Function, Dover Publications, New York, 1974 (ISBN 978-0-486-41740-0), p. 120.

Links

Seiichi Manyama, Table of n, a(n) for n = 1..1000

R. P. Brent, Asymptotic approximation of central binomial coefficients with rigorous error bounds, arXiv:1608.04834 [math.NA], 2016.

Simon Plouffe, On the values of the functions zeta and gamma, arXiv preprint arXiv:1310.7195, 2013.

Eric Weisstein's World of Mathematics, Riemann-Siegel Function

Formula

a(n) is the denominator of (-1)^n*BernoulliB(2*n, 1/2)/(4*n*(2*n-1)).

Example

RiemannSiegelTheta(t) = -Pi/8 + t*(-1/2 - log(2)/2 - log(Pi)/2 - log(t^(-1))/2) + 1/(48*t) + 7/(5760*t^3) + 31/(80640*t^5) + ...

Mathematica

a[n_] := (-1)^n*BernoulliB[2*n, 1/2]/(4*n*(2*n-1)) // Denominator; Table[a[n], {n, 1, 16}] (* Jean-François Alcover, Aug 04 2014 *)

Prog

(PARI) a(n) = denominator(subst(bernpol(2*n), x, 1/2)/(4*n*(2*n-1))); \\ Michel Marcus, Jun 20 2018

Crossrefs

Cf. A036282, A282898 (numerators), A282899.

Sequence in context: A364174 A222846 A265666 * A057868 A269179 A276098

Adjacent sequences: A114718 A114719 A114720 * A114722 A114723 A114724

Keyword

nonn,frac

Author

Eric W. Weisstein, Dec 27 2005

Status

approved