A243264 Decimal expansion of the generalized Glaisher-Kinkelin constant A(4).

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

Offset

0,1

Comments

Also known as the 4th Bendersky constant.

References

Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 2.15 Glaisher-Kinkelin constant, p. 137.

Links

G. C. Greubel, Table of n, a(n) for n = 0..2002

Eric Weisstein's MathWorld, Glaisher-Kinkelin Constant.

Formula

A(k) = exp(B(k+1)/(k+1)*H(k)-zeta'(-k)), where B(k) is the k-th Bernoulli number and H(k) the k-th harmonic number.

A(4) = exp(-zeta'(-4)) = exp(-3*zeta(5)/(4*Pi^4)).

A(4) = exp((B(4)/4)*(zeta(5)/zeta(4))). - G. C. Greubel, Dec 31 2015

Example

0.9920479745250402600134369776254433567369...

Mathematica

RealDigits[Exp[-3*Zeta[5]/(4*Pi^4)], 10, 98] // First
RealDigits[Exp[N[(BernoulliB[4]/4)*(Zeta[5]/Zeta[4]), 100]]] // First (* G. C. Greubel, Dec 31 2015 *)

Prog

(PARI) exp(-3*zeta(5)/(4*Pi^4)) \\ Stefano Spezia, Dec 01 2024

Crossrefs

Cf. A255323, A259069.

Cf. A019727, A074962, A243262, A243263, A243265, A266553, A266554, A266555, A266556, A266557, A266558, A266559, A260662, A266560, A266562, A266563, A266564, A266565, A266566, A266567.

Sequence in context: A371996 A120704 A021506 * A133250 A344727 A199623

Adjacent sequences: A243261 A243262 A243263 * A243265 A243266 A243267

Keyword

nonn,cons

Author

Jean-François Alcover, Jun 02 2014

Status

approved