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A355977 Decimal expansion of 2*zeta(3/2)^4/(3*sqrt(2*Pi)*zeta(3)). 1
1, 0, 3, 0, 4, 7, 1, 7, 4, 3, 9, 5, 0, 0, 1, 3, 8, 7, 0, 9, 9, 6, 8, 8, 9, 2, 1, 4, 1, 1, 7, 1, 7, 6, 3, 5, 7, 0, 4, 3, 7, 3, 5, 9, 9, 8, 0, 2, 0, 7, 9, 4, 6, 6, 2, 3, 8, 5, 0, 4, 5, 3, 5, 9, 2, 8, 5, 1, 6, 6, 8, 4, 5, 2, 7, 4, 3, 8, 0, 3, 2, 8, 6, 7, 8, 5, 4, 5, 3, 3, 2, 6, 9, 8, 5, 4, 9, 0, 3, 0, 8, 0, 6, 8, 1 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET
2,3
COMMENTS
The constant c_2 in the asymptotic mean of the squared error of the second moment of the Riemann zeta function on the critical line Re(z) = 1/2: Integral_{t=2..T} E(t)^2 dt ~ c_2 * T^(3/2), where E(t) = Integral_{t=0..T} |zeta(1/2 + i*t)|^2 dt - (log(T) - c) * T, and c is A355976.
REFERENCES
Steven R. Finch, Mathematical Constants II, Cambridge University Press, 2018, p. 177.
LINKS
Tom Meurman, On the mean square of the Riemann zeta-function, The Quarterly Journal of Mathematics, Vol. 38, No. 3 (1987), pp. 337-343.
FORMULA
Equals (2/(3*sqrt(2*Pi)) * Sum_{k>=1} d(k)^2/k^(3/2), where d(k) = A000005(k) is the number of divisors of k.
EXAMPLE
10.30471743950013870996889214117176357043735998020794...
MATHEMATICA
RealDigits[2*Zeta[3/2]^4/(3*Sqrt[2*Pi]*Zeta[3]), 10, 100][[1]]
CROSSREFS
Sequence in context: A190181 A145092 A210878 * A356581 A367480 A320373
KEYWORD
nonn,cons
AUTHOR
Amiram Eldar, Jul 22 2022
STATUS
approved

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Last modified April 24 04:14 EDT 2024. Contains 371918 sequences. (Running on oeis4.)