OFFSET
0,1
COMMENTS
This number is transcendental from a result of Schneider on elliptic integrals.
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.
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
EXAMPLE
2.428650647887581611819....
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 *)
PROG
(PARI) gamma(1/3)^3/2^(4/3)/Pi
CROSSREFS
KEYWORD
cons,nonn
AUTHOR
Benoit Cloitre, Jan 08 2006
STATUS
approved