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A019704 Decimal expansion of sqrt(Pi)/2. 8
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).

Michael Penn, An interesting approach to the Gaussian integral, YouTube video, 2021.

Index to sequences related to the Gamma function

FORMULA

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

Equals Integral_{x=0..infinity} exp(-x^2) dx = Integral_{x=0..infinity} exp(-(x - 1/x)^2) dx = Integral_{x=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)

Equals Integral_{x=0..oo} sin(x^2)^2/x^2 dx. - Amiram Eldar, Aug 21 2020

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: A202497 A195708 A340168 * 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 April 20 06:59 EDT 2021. Contains 343125 sequences. (Running on oeis4.)