A081760 Decimal expansion of Gamma(1/3)*Gamma(5/6)/Gamma(1/6).

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

Offset

0,1

Comments

Conjectured to be the value of Landau's constant L.

References

Steven R. Finch, Mathematical Constants, Encyclopedia of Mathematics and its Applications, vol. 94, Cambridge University Press, 2003, Section 7.1, p. 456.

Links

Harry J. Smith, Table of n, a(n) for n = 0..1000

Eric Weisstein's World of Mathematics, Landau constant.

Index entries for transcendental numbers.

Formula

Equals 2^(5/3) * Pi^2 / (3 * Gamma(1/3)^3). - Vaclav Kotesovec, Jun 10 2018

Equals Product_{k>=0} (18*k^2 + 21*k + 3) / (18*k^2 + 21*k + 5). - Antonio Graciá Llorente, May 02 2024

Example

0.5432589653429767...

Mathematica

Gamma[1/3]*Gamma[5/6]/Gamma[1/6] // RealDigits[#, 10, 104]& // First (* Jean-François Alcover, Feb 25 2014 *)

Prog

(PARI)  default(realprecision, 1080); x=gamma(1/3)*gamma(5/6)/gamma(1/6); d=0; for (n=0, 1000, x=(x-d)*10; d=floor(x); write("b081760.txt", n, " ", d));  \\ Harry J. Smith, Apr 13 2009
(PARI) 2^(5/3)*Pi^2/(3*gamma(1/3)^3) \\ Charles R Greathouse IV, Jul 14 2026

Crossrefs

Sequence in context: A003561 A201327 A329457 * A261218 A094097 A145330

Adjacent sequences: A081757 A081758 A081759 * A081761 A081762 A081763

Keyword

cons,nonn,changed

Author

Benoit Cloitre, Apr 09 2003

Extensions

Revised by Sean A. Irvine, Nov 09 2025

Status

approved