A215722 -id:A215722 - cp's OEIS frontend

A385742 Decimal expansion of (Pi/32) * (-1/2- zeta'(4/3)/zeta(4/3)).

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

Offset: 0

Graph
List
Refs
Listen
History
Text
Internal format

Mats Granvik, Jul 08 2025

nonn
cons

Let epsilon = 1/3, so that s = 1 + epsilon, then the constant appears to be equal to: (Pi/32) * (4 + 1/((s-2)*(s-1)) - zeta'(s)/zeta(s)) = Integral_{t=0..oo} (1 - 12*t^2)/((1 + 4*t^2)^3) * Integral_{sigma=1/2..oo} Re(log(zeta(sigma + epsilon + i*t))) dsigma dt. The agreement appears to hold for -3 < epsilon < 1.

			0.1943911932990676252341639336900663506249738278660...

Cf. A215722, A384541.

epsilon = 1/3; s = 1 + epsilon; RealDigits[Pi/32*(4 + 1/((-2 + s)*(-1 + s)) - Zeta'[s]/ Zeta[s]), 10, 105][[1]]

cp's OEIS Frontend

A385742 Decimal expansion of (Pi/32) * (-1/2- zeta'(4/3)/zeta(4/3)).

Views

Author

Keywords

Comments

Examples

Crossrefs

Programs

Mathematica