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A327995
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Decimal expansion of Gamma(3/4)/Pi^(1/4).
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1
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9, 2, 0, 4, 4, 1, 7, 8, 7, 8, 3, 5, 5, 9, 0, 9, 8, 3, 9, 3, 4, 9, 1, 7, 1, 3, 0, 7, 4, 9, 9, 9, 0, 9, 8, 1, 2, 2, 9, 4, 9, 8, 9, 2, 0, 2, 0, 9, 1, 5, 1, 3, 4, 2, 2, 5, 3, 3, 0, 0, 0, 5, 8, 9, 1, 8, 1, 5, 3, 5, 0, 3, 7, 4, 1, 5, 1, 3, 1, 3, 4, 3, 5, 5, 4, 9
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OFFSET
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0,1
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COMMENTS
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The function df(x) = 2^(x/2)*(2/Pi)^(sin(Pi*x/2)^2/2)*Gamma(x/2+1) interpolates the double factorials A006882 and extends them analytically. df(-1/2) is the given constant. Extending also the notation this can be written as (-1/2)!! = (-1/4)!/Pi^(1/4).
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LINKS
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FORMULA
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Equals (-1/4)!/Pi^(1/4).
Equals Pi^(3/4)*sqrt(2)/Gamma(1/4).
Equals Product_{k>=0} ((4*k+1)*(4*k+4)/((4*k+2)*(4*k+3)))^A010060(k) (Allouche et al., 2019). (End)
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EXAMPLE
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0.92044178783559098393491713074999098122949892...
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MAPLE
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Digits := 100: GAMMA(3/4)/Pi^(1/4)*10^86:
ListTools:-Reverse(convert(floor(%), base, 10));
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MATHEMATICA
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RealDigits[Gamma[3/4]/Surd[Pi, 4], 10, 120][[1]] (* Harvey P. Dale, Jun 13 2020 *)
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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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