A190732 - OEIS

%I #64 Oct 20 2024 02:33:09

%S 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,

%T 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,

%U 8,4,9,3,6,8,8,2

%N Decimal expansion of 2/sqrt(Pi).

%C According to Weisstein, some mathematicians define erf(z) without reference to this constant.

%C 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

%C Limit_{n->oo} 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

%C 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

%D Chi Keung Cheung et al., Getting Started with Mathematica, 2nd Ed. New York: J. Wiley (2005) p. 79.

%D C. N. Pickworth, The Slide Rule, 24th Ed., Pitman, London (1945), p 53, Gauge Points.

%H G. C. Greubel, <a href="/A190732/b190732.txt">Table of n, a(n) for n = 1..5000</a>

%H S. R. Finch, <a href="http://arxiv.org/abs/1111.4976">Mean width of a regular simplex</a>, arxiv:1111.4976 [math.MG], 2016, mu_2.

%H International Slide Rule Museum, <a href="https://www.sliderulemuseum.com/SR_Terms.htm#C">Slide Rule Terms, Glossary and Encyclopedia</a>, entry for "C".

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Erf.html">Erf</a>

%H <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>

%F Equals Sum_{n>=0} (-1)^n*Gamma((n+1)/2)/Gamma(n/2+1). - _Jean-François Alcover_, Jun 12 2013

%F Equals 1/A019704. - _Michel Marcus_, Jan 09 2017

%F Equals Limit_{n->infinity} A285388(n)/A285389(n). - _Ralf Steiner_, Apr 22 2017

%e 1.12837916709551257...

%t RealDigits[2/Sqrt[Pi], 10, 100][[1]]

%t RealDigits[Limit[2^(1 - 2 m^2) m Binomial[2 m^2, m^2], m -> Infinity], 10, 100][[1]] (* _Ralf Steiner_, Apr 22 2017 *)

%o (PARI) 2/sqrt(Pi) \\ _G. C. Greubel_, Jan 09 2017

%Y Cf. A002161, A019704, A285388, A285389.

%K nonn,cons

%O 1,3

%A _Alonso del Arte_, May 17 2011