A081760 Decimal expansion of the conjectured Landau's constant L.

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

Author

Benoit Cloitre, Apr 09 2003

Keywords

• cons
• nonn

Comments

Terms are computed using the conjectured formula.

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.

Programs

Mathematica

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

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

Formula

It is conjectured that L = 0.5432589653429767... = Gamma(1/3)*Gamma(5/6)/Gamma(1/6).

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

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