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A068467
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Decimal expansion of (1/4)! = Gamma(5/4).
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16
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9, 0, 6, 4, 0, 2, 4, 7, 7, 0, 5, 5, 4, 7, 7, 0, 7, 7, 9, 8, 2, 6, 7, 1, 2, 8, 8, 9, 6, 6, 9, 1, 8, 0, 0, 0, 7, 4, 8, 7, 9, 1, 9, 2, 0, 7, 2, 0, 0, 1, 6, 3, 6, 6, 8, 5, 8, 3, 4, 4, 4, 9, 9, 8, 9, 2, 4, 7, 9, 8, 1, 0, 8, 8, 4, 6, 8, 2, 2, 8, 0, 4, 0, 4, 5, 9, 0, 0, 3, 4, 1, 8, 0, 8, 4, 6, 0, 7, 5, 0, 9, 0, 3, 6
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OFFSET
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0,1
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LINKS
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FORMULA
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2^(3/4)*(2/e^(16*Pi) + 1)* Pi^(3/4)/(2^(13/16)/(sqrt(2) - 1)^(1/4) + 2^(1/4) + 1) is a very good approximation (~88 digits) which becomes exact if you replace (2/e^(16*Pi) + 1) by EllipticTheta[3,0,exp(-(16*Pi))]. [R. W. Gosper, Posting to Math Fun Mailing List, Dec 27 2011.]
Equals 2^(-5/4)*Pi^(3/4)*Product_{k>=1} tanh(Pi*k/2). - Keshav Raghavan, Aug 25 2016
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EXAMPLE
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0.906402477055477077982671288966918000748791920720...
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MAPLE
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MATHEMATICA
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RealDigits[Gamma[5/4], 10, 120][[1]] (* Harvey P. Dale, Aug 23 2013 *)
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PROG
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(Magma) SetDefaultRealField(RealField(100)); Gamma(5/4); // G. C. Greubel, Mar 11 2018
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CROSSREFS
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KEYWORD
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AUTHOR
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EXTENSIONS
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Removed leading zero and adjusted offset, R. J. Mathar, Feb 06 2009
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STATUS
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approved
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