A282898 Numerator of the coefficients of the series expansion of the Riemann-Siegel theta function at infinity.

1, 7, 31, 127, 511, 1414477, 8191, 118518239, 5749691557, 91546277357, 23273283019, 1982765468311237, 22076500342261, 455371239541065869, 925118910976041358111, 16555640865486520478399, 1302480594081611886641, 904185845619475242495834469891

Offset: 1

Author

Mats Granvik and Robert G. Wilson v, Feb 24 2017

Keywords

• nonn
• frac

Comments

See "RiemannSiegelTheta" in the help file of Mathematica, Series expansion at infinity.

Links

• Seiichi Manyama, Table of n, a(n) for n = 1..275
• Richard P. Brent, On asymptotic approximations to the log-Gamma and Riemann-Siegel theta functions, arXiv:1609.03682 [math.NA], 2016.
• Eric Weisstein's World of Mathematics, Riemann-Siegel Functions
• Wikipedia, Riemann-Siegel theta function
• Wolfram Language and System, RiemannSiegelTheta

Crossrefs

Cf. A114721, A282899.

Differs from A036282.

Programs

Mathematica

Numerator[ DeleteCases[ CoefficientList[ CoefficientList[ Series[ RiemannSiegelTheta[ t], {t, Infinity, 41}], 1/t^_] + Pi/8 + t/2 + t*Log[2]/2 + t*Log[Pi]/2 + t*Log[1/t]/2, 1/t][[1]], 0]]