A371930 Decimal expansion of Pi^(1/2)*Gamma(1/14)/(7*Gamma(4/7)).

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

Offset: 1

Author

Takayuki Tatekawa, Apr 12 2024

Keywords

• nonn
• cons

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

Examples

			2.191450245201078533946264870311...
		

Links

• Takayuki Tatekawa, Table of n, a(n) for n = 1..10001

Crossrefs

Cf. A085565, A113477, A262427, A371824.

Programs

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]]

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