A074758 Decimal expansion of zeta'(1/2)/zeta(1/2).

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

Offset

1,1

References

S. J. Patterson, "An introduction to the theory of the Riemann Zeta-function", Cambridge studies in advanced mathematics 14, p. 29.

Links

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

Formula

Equals log(8*Pi)/2 + EulerGamma/2 + Pi/4 = 2.6860917...

Equals (1/2) * (log(Pi) - Gamma'(1/4) / Gamma(1/4)). - Mats Granvik, Jul 30 2017

Example

2.686091709612832791116478748724871144507269625811776921584451315495547282857339...

Mathematica

RealDigits[Zeta'[1/2]/Zeta[1/2], 10, 120][[1]] (* Vaclav Kotesovec, Feb 18 2021 *)

Prog

(PARI) log(8*Pi)/2 + Euler/2 + Pi/4 \\ Michel Marcus, Jul 30 2017

Crossrefs

Cf. A059750.

Sequence in context: A145500 A247572 A065129 * A228163 A029671 A278081

Adjacent sequences: A074755 A074756 A074757 * A074759 A074760 A074761

Keyword

cons,nonn

Author

Benoit Cloitre, Sep 28 2002

Status

approved