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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 G. C. Greubel, Table of n, a(n) for n = 1..5000 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 Index entries for transcendental numbers 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 Cf. A002161, A019704, A285388, A285389. Sequence in context: A256921 A133840 A337570 * A081349 A111445 A076696 Adjacent sequences: A190729 A190730 A190731 * A190733 A190734 A190735 KEYWORD nonn,cons AUTHOR Alonso del Arte, May 17 2011 STATUS approved

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Last modified August 13 09:04 EDT 2024. Contains 375118 sequences. (Running on oeis4.)