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A019704 Decimal expansion of sqrt(Pi)/2. 5
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 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

0,1

REFERENCES

C. C. Clawson, The Beauty and Magic of Numbers. New York: Plenum Press (1996): 210.

LINKS

Ivan Panchenko, Table of n, a(n) for n = 0..1000

I. S. Gradsteyn, I. M. Ryzhik, Table of integrals, series and products, (1980), page 420 (formulas 3.757.1, 3.757.2).

Index to sequences related to the Gamma function

FORMULA

(1/2)! = Gamma(3/2) = sqrt(Pi)/2. - Benoit Cloitre, Apr 24 2003

Equals Integral_{x>=0} exp(-x^2) dx, or integral_{0, infinity} exp(-(x - 1/x)^2) dx, or also integral_{0, 1} sqrt(log(1/x)) dx. - Jean-Fran├žois 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)

EXAMPLE

sqrt(Pi)/2 = 0.886226925452758013649...

MAPLE

evalf(sqrt(Pi)/2, 120); # Muniru A Asiru, Sep 22 2018

MATHEMATICA

RealDigits[Sqrt[Pi]/2, 10, 100][[1]] (* Alonso del Arte, Aug 15 2012 *)

PROG

(PARI) gammah(1) \\ Michel Marcus, Feb 11 2016

(PARI) sqrt(Pi)/2 \\ Michel Marcus, Feb 11 2016

(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

CROSSREFS

Cf. A003881.

Sequence in context: A153619 A202497 A195708 * A140976 A253270 A021057

Adjacent sequences:  A019701 A019702 A019703 * A019705 A019706 A019707

KEYWORD

nonn,cons

AUTHOR

N. J. A. Sloane

STATUS

approved

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Last modified March 23 04:46 EDT 2019. Contains 321422 sequences. (Running on oeis4.)