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A002161 Decimal expansion of square root of Pi.
(Formerly M4332 N1814)
71
1, 7, 7, 2, 4, 5, 3, 8, 5, 0, 9, 0, 5, 5, 1, 6, 0, 2, 7, 2, 9, 8, 1, 6, 7, 4, 8, 3, 3, 4, 1, 1, 4, 5, 1, 8, 2, 7, 9, 7, 5, 4, 9, 4, 5, 6, 1, 2, 2, 3, 8, 7, 1, 2, 8, 2, 1, 3, 8, 0, 7, 7, 8, 9, 8, 5, 2, 9, 1, 1, 2, 8, 4, 5, 9, 1, 0, 3, 2, 1, 8, 1, 3, 7, 4, 9, 5, 0, 6, 5, 6, 7, 3, 8, 5, 4, 4, 6, 6, 5 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
Also Gamma(1/2). - Franklin T. Adams-Watters, Apr 07 2006
The integral of the Gaussian function exp(-x^2) over the real line. - Richard Chapling (r.chappers(AT)gmail.com), Jun 05 2008
Also equals the average distance between two points in two dimensions where coordinates are independent normally distributed random variables with mean 0 and variance 1. - Jean-François Alcover, Oct 31 2014, after Steven Finch
Also diameter of a sphere whose surface area equals Pi^2. More generally, the square root of x is also the diameter of a sphere whose surface area equals x*Pi. - Omar E. Pol, Nov 11 2018
REFERENCES
George Boros and Victor H. Moll, Irresistible integrals, Cambridge University Press (2006), p. 190.
W. E. Mansell, Tables of Natural and Common Logarithms. Royal Society Mathematical Tables, Vol. 8, Cambridge Univ. Press, 1964, p. XVIII.
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
LINKS
Donald Knuth, Why pi?, Christmas Tree lecture, Dec 06 2010 (video).
FORMULA
Equals (1/2) * Sum_{n>=0} ((-1)^n * (4*n+1) * (1/8)^(n+1) * (2^(n+1))^3 * Gamma(n+1/2)^3 / Gamma(n+1)^3). - Alexander R. Povolotsky, Mar 25 2013
Equals Integral_{x=0..1} 1/sqrt(-log(x)) dx. - Jean-François Alcover, Apr 29 2013
Equals Sum_{k>=0} (k+1/2)!/(k+2)!. - Amiram Eldar, Jun 19 2023
Equals Integral_{x=0..oo} exp(-x)/sqrt(x) dx. - Michal Paulovic, Sep 24 2023
EXAMPLE
1.7724538509055160272981674833411451827975494561223871282138...
MAPLE
evalf(sqrt(Pi), 120); # Muniru A Asiru, Nov 11 2018
MATHEMATICA
RealDigits[N[Sqrt[Pi], 120]][[1]] (* Richard Chapling (r.chappers(AT)gmail.com), Jun 05 2008 *)
PROG
(PARI) default(realprecision, 20080); x=sqrt(Pi); for (n=1, 20000, d=floor(x); x=(x-d)*10; write("b002161.txt", n, " ", d)); \\ Harry J. Smith, May 01 2009
(Magma) R:= RealField(100); Sqrt(Pi(R)); // G. C. Greubel, Mar 10 2018
CROSSREFS
Cf. decimal expansions of Gamma(1/k): A073005 (k=3), A068466 (k=4), A175380 (k=5), A175379 (k=6), A220086 (k=7), A203142 (k=8).
Sequence in context: A102400 A144860 A113810 * A083871 A255272 A335929
KEYWORD
nonn,cons
AUTHOR
EXTENSIONS
More terms from Franklin T. Adams-Watters, Apr 07 2006
STATUS
approved

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Last modified February 29 17:23 EST 2024. Contains 370427 sequences. (Running on oeis4.)