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

Author

Eric W. Weisstein, Dec 27 2005

Keywords

• nonn
• frac

Examples

			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) + ...
		

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

Crossrefs

Cf. A036282, A282898 (numerators), A282899.

Programs

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 *)

PARI

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

Formula

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