A243999 Decimal expansion of B (negated), a constant related to Glaisher's constant A and the Gaussian unitary ensemble hypothesis.

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

Offset

0,1

References

Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 2.15 Glaisher-Kinkelin constant, p. 140.

Links

Table of n, a(n) for n=0..99.

Dan Bump, The Gaussian Unitary Ensemble Hypothesis.

Eric Weisstein's MathWorld, Glaisher-Kinkelin Constant.

Eric Weisstein's MathWorld, Random Matrix.

Formula

B = 1/24*(log(2) - 36*log(A) + 3), where A is Glaisher's constant.

B = 1/24*log(2) + 3/2*zeta'(-1).

exp(2*B) = 2^(1/12)*exp(1/4)*A^(-3).

Example

-0.2192505830273453392618281519700802738...

Mathematica

B = 1/24*(Log[2] - 36*Log[Glaisher] + 3); RealDigits[B, 10, 100] // First

Prog

(PARI) log(2)/24 + 3*zeta'(-1)/2 \\ Amiram Eldar, Jul 25 2024

Crossrefs

Cf. A074962 (A), A084448 (zeta'(-1)).

Sequence in context: A030327 A095890 A292827 * A223141 A021460 A090884

Adjacent sequences: A243996 A243997 A243998 * A244000 A244001 A244002

Keyword

nonn,cons

Author

Jean-François Alcover, Jun 17 2014

Status

approved