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A110544
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Decimal expansion of -Integral {x=1..2} log gamma(x) dx.
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3
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0, 8, 1, 0, 6, 1, 4, 6, 6, 7, 9, 5, 3, 2, 7, 2, 5, 8, 2, 1, 9, 6, 7, 0, 2, 6, 3, 5, 9, 4, 3, 8, 2, 3, 6, 0, 1, 3, 8, 6, 0, 2, 5, 2, 6, 3, 6, 2, 2, 1, 6, 5, 8, 7, 1, 8, 2, 8, 4, 8, 4, 5, 9, 5, 1, 7, 2, 3, 4, 3, 0, 4, 0, 7, 2, 7, 3, 9, 6, 0, 2, 3, 0, 5, 2, 5, 6, 7, 0, 1, 3, 6, 4, 0, 4, 5, 8, 0, 2, 3, 7, 7, 9, 9, 4, 3
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OFFSET
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0,2
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LINKS
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FORMULA
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Equals Sum_{k>=2} (1/(k + 1) - 1/(2*k))*(zeta(k)-1).
Equals Integral_{x=0..1} (1/2 - 1/(1 - x) - 1/log(x)) dx/log(x). (End)
Equals -Integral_{x=1..oo} ({x}-1/2)/x dx, where {.} is the fractional part [Nahin]. - R. J. Mathar, May 16 2024
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EXAMPLE
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0.081061466795327258219670263594382360138602526362216587182848459...
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MATHEMATICA
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RealDigits[ N[ -Integrate[ Log[ Gamma[ x]], {x, 1, 2}], 128], 10, 128]
RealDigits[ 1/2*Log[2*Pi]-1, 10, 105] // First // Prepend[#, 0]& (* Jean-François Alcover, Jun 10 2013 *)
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PROG
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(PARI) -intnum(x=1, 2, log(gamma(x))) \\ Michel Marcus, Jul 05 2020
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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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