A371824 Decimal expansion of Pi^(1/2)*Gamma(1/10)/(5*Gamma(3/5)).

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

Offset: 1

Author

Takayuki Tatekawa, Apr 07 2024

Keywords

• nonn
• cons

Comments

Constants from generalized Pi integrals: the case of n=10.

Examples

			2.264617395043150744291188990313...
		

Links

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

Crossrefs

Cf. A085565, A113477, A262427.

Programs

Mathematica

RealDigits[2*Sqrt[Pi]/10*Gamma[1/10]/Gamma[3/5], 10, 5001][[1]]
RealDigits[GoldenRatio * Gamma[1/5] * Gamma[2/5]^2 / (2^(6/5) * Sqrt[5] * Pi), 10, 120][[1]] (* Vaclav Kotesovec, Apr 07 2024 *)

Formula

Equals 2*Integral_{x=0..1} dx/sqrt(1-x^10).

Equals phi * Gamma(1/5) * Gamma(2/5)^2 / (2^(6/5) * sqrt(5) * Pi), where phi = A001622 is the golden ratio. - Vaclav Kotesovec, Apr 07 2024