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A114721 Denominator of expansion of RiemannSiegelTheta[t] about infinity. 0
48, 5760, 80640, 430080, 1216512, 1476034560, 2555904, 8021606400, 64012419072, 131491430400, 3472883712, 25282593423360, 20132659200, 25222195445760, 2675794690179072, 2172909854392320, 6803228196864 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

REFERENCES

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

LINKS

Table of n, a(n) for n=0..16.

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

(-1)^(n+1)*BernoulliB(2*(n+1), 1/2)/(4*(n+1)*(2*n+1)).

EXAMPLE

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

MATHEMATICA

a[n_] := (-1)^(n+1)*BernoulliB[2*(n+1), 1/2]/(4*(n+1)*(2*n+1)) // Denominator; Table[a[n], {n, 0, 16}] (* Jean-Fran├žois Alcover, Aug 04 2014 *)

CROSSREFS

Cf. A036282.

Sequence in context: A208793 A174755 A222846 * A057868 A233242 A130417

Adjacent sequences:  A114718 A114719 A114720 * A114722 A114723 A114724

KEYWORD

nonn,frac

AUTHOR

Eric W. Weisstein, Dec 27, 2005

STATUS

approved

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Last modified November 22 18:41 EST 2014. Contains 249807 sequences.