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A244920
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Decimal expansion of 2*log(1+sqrt(2)), the integral over the square [0,1]x[0,1] of 1/sqrt(x^2+y^2) dx dy.
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12
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1, 7, 6, 2, 7, 4, 7, 1, 7, 4, 0, 3, 9, 0, 8, 6, 0, 5, 0, 4, 6, 5, 2, 1, 8, 6, 4, 9, 9, 5, 9, 5, 8, 4, 6, 1, 8, 0, 5, 6, 3, 2, 0, 6, 5, 6, 5, 2, 3, 2, 7, 0, 8, 2, 1, 5, 0, 6, 5, 9, 1, 2, 1, 7, 3, 0, 6, 7, 5, 4, 3, 6, 8, 4, 4, 4, 0, 5, 2, 1, 7, 5, 6, 6, 7, 4, 1, 3, 7, 8, 3, 8, 2, 0, 5, 1, 2, 0, 8, 5, 7
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OFFSET
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1,2
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COMMENTS
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Number field regulator of the cyclotomic number field Q(zeta_8), where zeta_8 = sqrt(i), an eighth root of 1. - Alonso del Arte, Mar 11 2017
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LINKS
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FORMULA
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Equals 2*arcsinh(1).
Equals Integral_{x>=1} 1/(x*(1+x)^(1/2)) dx. - Pointed out by Robert FERREOL.
Equals Integral_{x>=1} arcsinh(x)/x^2 dx. - Amiram Eldar, Jun 26 2021
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EXAMPLE
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1.7627471740390860504652186499595846180563206565232708215065912173...
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MATHEMATICA
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RealDigits[2 * Log[1 + Sqrt[2]], 10, 101] // First
RealDigits[NumberFieldRegulator[Sqrt[I]], 10, 100][[1]] (* Alonso del Arte, Mar 11 2017 *)
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PROG
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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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