A355976 Decimal expansion of 1 + log(2*Pi) - 2*gamma, where gamma is Euler's constant (A001620).

1, 6, 8, 3, 4, 4, 5, 7, 3, 6, 6, 0, 6, 2, 7, 9, 7, 6, 2, 3, 4, 7, 6, 3, 5, 2, 9, 2, 6, 4, 6, 4, 3, 0, 4, 1, 7, 6, 3, 8, 4, 7, 6, 2, 7, 5, 3, 9, 5, 7, 1, 9, 6, 2, 8, 0, 2, 2, 7, 6, 8, 6, 1, 1, 1, 9, 5, 7, 9, 5, 9, 3, 8, 2, 9, 9, 1, 9, 1, 4, 5, 3, 5, 1, 5, 5, 9, 2, 4, 7, 0, 6, 8, 8, 4, 1, 4, 8, 9, 6, 2, 1, 4, 7, 4

Offset

1,2

Comments

The constant c in the asymptotic formula for the second moment of the Riemann zeta function on the critical line Re(z) = 1/2: Integral_{t=0..T} |zeta(1/2 + i*t)|^2 dt ~ (log(T) - c) * T.

References

Steven R. Finch, Mathematical Constants II, Cambridge University Press, 2018, p. 177.

Links

Table of n, a(n) for n=1..105.

F. V. Atkinson, The mean value of the zeta-function on the critical line, The Quarterly Journal of Mathematics, Vol. os-10, No. 1 (1939), pp. 122-128.

A. E. Ingham, Mean-value theorems in the theory of the Riemann zeta-function, Proceedings of the London Mathematical Society, Vol. s2-27, No. 1 (1928), pp. 273-300.

E. C. Titchmarsh, On van der Corput's method and the zeta-function of Riemann (V), The Quarterly Journal of Mathematics, Vol. os-5, No. 1 (1934), pp. 195-210.

Example

1.68344573660627976234763529264643041763847627539571...

Mathematica

RealDigits[1 + Log[2*Pi] - 2*EulerGamma, 10, 100][[1]]

Crossrefs

Cf. A001620, A053510, A355977.

Sequence in context: A103430 A097880 A196768 * A021598 A021940 A316256

Adjacent sequences: A355973 A355974 A355975 * A355977 A355978 A355979

Keyword

nonn,cons

Author

Amiram Eldar, Jul 22 2022

Status

approved