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A246843 Decimal expansion of C, a constant associated with the estimation of the maximum of |zeta(1+i*t)|. 2
0, 8, 9, 3, 2, 6, 5, 2, 2, 3, 4, 3, 5, 5, 1 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Table of n, a(n) for n=0..14.

Steven R. Finch, Errata and Addenda to Mathematical Constants, p. 28.

Tadej Kotnik, Computational estimation of the constant β(1) characterizing the order of ζ(1 + it), Math. Comp. 77: 1713-1723, 2008.

FORMULA

1 - log(2) + integral_{0..2} log(BesselI(0, t))/t^2 dt + integral_{2..infinity} (log(BesselI(0, t)) - t)/t^2 dt.

EXAMPLE

-0.089326522343551...

MATHEMATICA

digits = 15; precision = 200; u0 = 10^8; du = 10^8; tail[u_] := -(1 + Log[2*Pi*u])/(2*u); Clear[f]; f[u_] := f[u] = 1 - Log[2] + NIntegrate[Log[BesselI[0, t]]/t^2, {t, 0, 2} , WorkingPrecision -> precision] + NIntegrate[(Log[BesselI[0, t]] - t)/t^2, {t, 2, u}, WorkingPrecision -> precision, MaxRecursion -> 20 ] + tail[u]; f[u0]; f[u = u0 + du]; While[RealDigits[f[u], 10, digits + 4] != RealDigits[f[u - du], 10, digits + 4], Print["u = ", u, " ", f[u]]; u = u + du]; Join[{0}, RealDigits[f[u], 10, digits] // First]

CROSSREFS

Cf. A074760, A104539, A104540, A242056.

Sequence in context: A203077 A197392 A021922 * A257438 A197826 A197755

Adjacent sequences:  A246840 A246841 A246842 * A246844 A246845 A246846

KEYWORD

nonn,cons,more

AUTHOR

Jean-François Alcover, Sep 05 2014

EXTENSIONS

Typo in the formula corrected by Vaclav Kotesovec, Sep 17 2014

STATUS

approved

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Last modified July 13 16:22 EDT 2020. Contains 335688 sequences. (Running on oeis4.)