|
| |
|
|
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.
|
|
1
| |
|
|
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; internal format)
|
|
|
|
OFFSET
| 0,2
|
|
|
REFERENCES
| S. J. Patterson, "An introduction to the theory of the Riemann Zeta-function", Cambridge studies in advanced mathematics 14, p. 34
|
|
|
LINKS
| Eric Weisstein's World of Mathematics, Li's Criterion
Eric Weisstein's World of Mathematics, Riemann Zeta Function Zeros
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.
Index entries for zeta function.
|
|
|
FORMULA
| -B = Gamma/2 + 1 - log(4*Pi)/2 = 0.0230957...
|
|
|
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: A173344 A020823 A021437 * A137914 A098989 A175315
Adjacent sequences: A074757 A074758 A074759 * A074761 A074762 A074763
|
|
|
KEYWORD
| cons,nonn
|
|
|
AUTHOR
| Benoit Cloitre (benoit7848c(AT)orange.fr), Sep 28 2002
|
| |
|
|
