A019704 Decimal expansion of sqrt(Pi)/2.
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
Offset: 0
Examples
sqrt(Pi)/2 = 0.886226925452758013649...
References
- C. C. Clawson, The Beauty and Magic of Numbers. New York: Plenum Press (1996): 210.
- Steven R. Finch, Mathematical Constants, Encyclopedia of Mathematics and its Applications, vol. 94, Cambridge University Press, 2003, Section 1.4.3, p. 22.
Links
- Ivan Panchenko, Table of n, a(n) for n = 0..1000
- I. S. Gradsteyn and I. M. Ryzhik, Table of integrals, series and products, (1980), page 420 (formulas 3.757.1, 3.757.2).
- Michael Penn, An interesting approach to the Gaussian integral, YouTube video, 2021.
- Eric Weisstein's World of Mathematics, Fractional Calculus.
- Index entries for transcendental numbers.
- Index to sequences related to the Gamma function.
Crossrefs
Cf. A003881.
Programs
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Magma
pi:=Sqrt(Pi(RealField(110)))/ 2; Reverse(Intseq(Floor(10^110*pi))); // Vincenzo Librandi, Feb 11 2016
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Maple
evalf(sqrt(Pi)/2,120); # Muniru A Asiru, Sep 22 2018
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Mathematica
RealDigits[Sqrt[Pi]/2, 10, 100][[1]] (* Alonso del Arte, Aug 15 2012 *)
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PARI
gammah(1) \\ Michel Marcus, Feb 11 2016
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PARI
sqrt(Pi)/2 \\ Michel Marcus, Feb 11 2016
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PARI
intnum(x=0, [oo, -2*I], sin(2*x)/sqrt(x)) \\ Gheorghe Coserea, Sep 23 2018
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PARI
intnum(x=[0,-1/2], [oo, 2*I], cos(2*x)/sqrt(x)) \\ Gheorghe Coserea, Sep 23 2018
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PARI
intnum(x=1, [oo, 1], exp(-(x-1/x)^2)*(1 + 1/x^2)) \\ Gheorghe Coserea, Sep 24 2018
Formula
Equals (1/2)! = Gamma(3/2). - Benoit Cloitre, Apr 24 2003
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 sqrt(A003881). - Michel Marcus, Aug 31 2014
From A.H.M. Smeets, Sep 22 2018: (Start)
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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