OFFSET
1,1
COMMENTS
Constants from generalized Pi integrals: the case of n=14.
In general, for k > 0, Integral_{x=0..1} 1/sqrt(1 - x^k) dx = 2^(2/k) * Gamma(1 + 1/k)^2 / Gamma(1 + 2/k) = 2^(2/k - 1) * Gamma(1/k)^2 / (k*Gamma(2/k)). - Vaclav Kotesovec, Apr 15 2024
LINKS
Takayuki Tatekawa, Table of n, a(n) for n = 1..10001
FORMULA
Equals 2*Integral_{x=0..1} dx/sqrt(1-x^14).
Equals Beta(1/14, 1/2) / 7. - Peter Luschny, Apr 14 2024
Equals Gamma(1/14)^2 / (7 * 2^(6/7) * Gamma(1/7)). - Vaclav Kotesovec, Apr 15 2024
EXAMPLE
2.191450245201078533946264870311...
MAPLE
Beta(1/14, 1/2) / 7: evalf(%, 90); # Peter Luschny, Apr 14 2024
MATHEMATICA
RealDigits[Sqrt[Pi]/7*Gamma[1/14]/Gamma[4/7], 10, 5001][[1]]
CROSSREFS
KEYWORD
nonn,cons
AUTHOR
Takayuki Tatekawa, Apr 12 2024
STATUS
approved