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A190732 Decimal expansion of 2/sqrt(Pi). 8
1, 1, 2, 8, 3, 7, 9, 1, 6, 7, 0, 9, 5, 5, 1, 2, 5, 7, 3, 8, 9, 6, 1, 5, 8, 9, 0, 3, 1, 2, 1, 5, 4, 5, 1, 7, 1, 6, 8, 8, 1, 0, 1, 2, 5, 8, 6, 5, 7, 9, 9, 7, 7, 1, 3, 6, 8, 8, 1, 7, 1, 4, 4, 3, 4, 2, 1, 2, 8, 4, 9, 3, 6, 8, 8, 2 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET
1,3
COMMENTS
According to Weisstein, some mathematicians define erf(z) without reference to this constant.
Also equals the average absolute value of the difference of two independent normally distributed random numbers with mean 0 and variance 1. - Jean-François Alcover, Oct 31 2014
Limit_{n->infinity} (2^(1 - 2 n^2) n binomial(2 n^2, n^2) is proper to compute this constant (and also Pi) in a base of power 2. - Ralf Steiner, Apr 23 2017
A gauge point marked "c" on slide rule calculating devices in the 20th century. The Pickworth reference notes its use "in calculating the contents of cylinders". - Peter Munn, Aug 14 2020
REFERENCES
Chi Keung Cheung et al., Getting Started with Mathematica, 2nd Ed. New York: J. Wiley (2005) p. 79.
C. N. Pickworth, The Slide Rule, 24th Ed., Pitman, London (1945), p 53, Gauge Points.
LINKS
S. R. Finch, Mean width of a regular simplex, arxiv:1111.4976 [math.MG], 2016, mu_2.
International Slide Rule Museum, Slide Rule Terms, Glossary and Encyclopedia, entry for "C".
Eric Weisstein's World of Mathematics, Erf
FORMULA
Equals Sum_{n>=0} (-1)^n*Gamma((n+1)/2)/Gamma(n/2+1). - Jean-François Alcover, Jun 12 2013
Equals 1/A019704. - Michel Marcus, Jan 09 2017
Equals Limit_{n->infinity} A285388(n)/A285389(n). - Ralf Steiner, Apr 22 2017
EXAMPLE
1.12837916709551257...
MATHEMATICA
RealDigits[2/Sqrt[Pi], 10, 100][[1]]
RealDigits[Limit[2^(1 - 2 m^2) m Binomial[2 m^2, m^2], m -> Infinity], 10, 100][[1]] (* Ralf Steiner, Apr 22 2017 *)
PROG
(PARI) 2/sqrt(Pi) \\ G. C. Greubel, Jan 09 2017
CROSSREFS
Sequence in context: A256921 A133840 A337570 * A081349 A111445 A076696
KEYWORD
nonn,cons
AUTHOR
Alonso del Arte, May 17 2011
STATUS
approved

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Last modified March 28 07:48 EDT 2024. Contains 371235 sequences. (Running on oeis4.)