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A371930
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Decimal expansion of Pi^(1/2)*Gamma(1/14)/(7*Gamma(4/7)).
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2
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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
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OFFSET
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1,1
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COMMENTS
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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
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LINKS
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FORMULA
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Equals 2*Integral_{x=0..1} dx/sqrt(1-x^14).
Equals Gamma(1/14)^2 / (7 * 2^(6/7) * Gamma(1/7)). - Vaclav Kotesovec, Apr 15 2024
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EXAMPLE
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2.191450245201078533946264870311...
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MAPLE
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MATHEMATICA
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RealDigits[Sqrt[Pi]/7*Gamma[1/14]/Gamma[4/7], 10, 5001][[1]]
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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