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A019704
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Decimal expansion of sqrt(Pi)/2.
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11
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8, 8, 6, 2, 2, 6, 9, 2, 5, 4, 5, 2, 7, 5, 8, 0, 1, 3, 6, 4, 9, 0, 8, 3, 7, 4, 1, 6, 7, 0, 5, 7, 2, 5, 9, 1, 3, 9, 8, 7, 7, 4, 7, 2, 8, 0, 6, 1, 1, 9, 3, 5, 6, 4, 1, 0, 6, 9, 0, 3, 8, 9, 4, 9, 2, 6, 4, 5, 5, 6, 4, 2, 2, 9, 5, 5, 1, 6, 0, 9, 0, 6, 8, 7, 4, 7, 5, 3, 2, 8, 3, 6, 9, 2, 7, 2, 3, 3, 2
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OFFSET
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0,1
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COMMENTS
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Also half integral of f(x)=sqrt(x) with 0<=x<=1 and half derivative of the same f(x). See Fractional Calculus link. - Andrea Pinos, Jul 15 2023
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REFERENCES
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C. C. Clawson, The Beauty and Magic of Numbers. New York: Plenum Press (1996): 210.
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LINKS
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FORMULA
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Equals Integral_{x=0..oo} exp(-x^2) dx = Integral_{x=0..oo} exp(-(x - 1/x)^2) dx = Integral_{x=0..1} sqrt(log(1/x)) dx. - Jean-François Alcover, Mar 28 2013
Equals Integral_{x >= 0} sin(2x)/sqrt(x) dx [Gradshteyn and Ryzhik].
Equals Integral_{x >= 0} cos(2x)/sqrt(x) dx [Gradshteyn and Ryzhik]. (End)
Equals Integral_{x=0..oo} sin(x^2)^2/x^2 dx. - Amiram Eldar, Aug 21 2020
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EXAMPLE
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sqrt(Pi)/2 = 0.886226925452758013649...
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MAPLE
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MATHEMATICA
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PROG
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(PARI) intnum(x=0, [oo, -2*I], sin(2*x)/sqrt(x)) \\ Gheorghe Coserea, Sep 23 2018
(PARI) intnum(x=[0, -1/2], [oo, 2*I], cos(2*x)/sqrt(x)) \\ Gheorghe Coserea, Sep 23 2018
(PARI) intnum(x=1, [oo, 1], exp(-(x-1/x)^2)*(1 + 1/x^2)) \\ Gheorghe Coserea, Sep 24 2018
(Magma) pi:=Sqrt(Pi(RealField(110)))/ 2; Reverse(Intseq(Floor(10^110*pi))); // Vincenzo Librandi, Feb 11 2016
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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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