A113477 Decimal expansion of Gamma(1/3)^3/(2^(4/3)*Pi).

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

Offset: 0

Author

Benoit Cloitre, Jan 08 2006

Keywords

• cons
• nonn

Comments

This number is transcendental from a result of Schneider on elliptic integrals.

Examples

			2.428650647887581611819....
		

Links

• G. C. Greubel, Table of n, a(n) for n = 0..5000
• Th. Schneider, Transzendenzuntersuchungen periodischer Funktionen, Journal für die reine und angewandte Mathematik (1935) Volume: 172, page 65-74.
• Th. Schneider, Arithmetische Untersuchungen elliptischer Integrale, Mathematische Annalen (1937) Volume: 113, page I-XIII.
• Index entries for transcendental numbers

Crossrefs

Cf. A085565.

Programs

Maple

Beta(1/6, 1/2)/3: evalf(%, 106); # Peter Luschny, Apr 15 2024

Mathematica

RealDigits[Gamma[1/3]^3/(Pi*2^(4/3)), 10, 5001][[1]] (* G. C. Greubel, Mar 12 2017 *)

PARI

gamma(1/3)^3/2^(4/3)/Pi

Formula

Equals Integral_{x>=1} dx/sqrt(4*x^3-4).

Equals 2*Integral_{x=0..1} dx/sqrt(1-x^6). - Takayuki Tatekawa, Apr 15 2024

Equals Beta(1/6, 1/2) / 3. - Peter Luschny, Apr 15 2024