A261829 Decimal expansion of -Zeta'(-1)/2.

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

Offset

0,2

References

Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 2.15 Glaisher-Kinkelin constant, p. 135.

Links

Table of n, a(n) for n=0..101.

Formula

Equals -Integral_{0..infinity} x*log(x)/(exp(2*Pi* x)-1) dx.

Equals 1/24 - log(A)/2, where A is the Glaisher-Kinkelin constant 1.282427... (A074962).

Equals A084448 / 2. - R. J. Mathar, Dec 17 2024

Example

0.08271057185022546460695983012139032138201819016760089183326...

Maple

evalf(-Zeta(1, -1)/2, 102); # Peter Luschny, Mar 24 2019

Mathematica

Join[{0}, RealDigits[1/24 - Log[Glaisher]/2, 10, 101] // First]

Prog

(PARI) -zeta'(-1)/2 \\ Michel Marcus, Mar 24 2019

Crossrefs

Cf. A074962.

Sequence in context: A091350 A099876 A153203 * A244686 A367479 A317386

Adjacent sequences: A261826 A261827 A261828 * A261830 A261831 A261832

Keyword

nonn,cons,easy

Author

Jean-François Alcover, Sep 02 2015

Extensions

New name by Peter Luschny, Mar 24 2019

Status

approved