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A074760 Decimal expansion of -B =(1/2)*sum(r in Z, 1/r/(1-r)) where Z is the set of zeros of the Riemann zeta-function which lie in the strip 0 <=Re(z)<=1. 9
0, 2, 3, 0, 9, 5, 7, 0, 8, 9, 6, 6, 1, 2, 1, 0, 3, 3, 8, 1, 4, 3, 1, 0, 2, 4, 7, 9, 0, 6, 4, 9, 5, 2, 9, 1, 6, 2, 1, 9, 3, 2, 1, 2, 7, 1, 5, 2, 0, 5, 0, 7, 5, 9, 5, 2, 5, 3, 9, 2, 0, 7, 2, 2, 1, 2, 9, 7, 1, 3, 5, 6, 4, 7, 6, 7, 2, 4, 5, 7, 9, 9, 7, 0, 7, 9, 8, 5, 6, 9, 5, 1, 1, 7, 0, 9, 8, 3, 3, 3, 6, 4, 3, 0 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

0,2

REFERENCES

H. M. Edwards, Riemann's Zeta Function, Dover Publications Inc. 1974, p. 160.

S. J. Patterson, "An introduction to the theory of the Riemann Zeta-function", Cambridge studies in advanced mathematics 14, p. 34

LINKS

Table of n, a(n) for n=0..103.

J. Sondow and C. Dumitrescu, A monotonicity property of Riemann's xi function and a reformulation of the Riemann Hypothesis, Periodica Math. Hungarica, 60 (2010), 37-40; see p. 3 in the link.

Eric Weisstein's World of Mathematics, Li's Criterion

Eric Weisstein's World of Mathematics, Riemann Zeta Function Zeros

Index entries for zeta function.

FORMULA

-B = Gamma/2 + 1 - log(4*Pi)/2 = 0.0230957...

EXAMPLE

0.023095708966121033814310247906495291621932127152050759525392...

MATHEMATICA

RealDigits[ N[ EulerGamma/2 + 1 - Log[4*Pi]/2, 100]] [[1]]

PROG

(PARI) Euler/2+1-log(4*Pi)/2 \\ Charles R Greathouse IV, Jan 26 2012

CROSSREFS

Cf. A002410 (nearest integer to imaginary part of n-th zeta zero), A195423 (twice the constant).

Sequence in context: A276994 A020823 A021437 * A137914 A098989 A175315

Adjacent sequences:  A074757 A074758 A074759 * A074761 A074762 A074763

KEYWORD

cons,nonn

AUTHOR

Benoit Cloitre, Sep 28 2002

STATUS

approved

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Last modified January 16 23:44 EST 2019. Contains 319206 sequences. (Running on oeis4.)