A190732 Decimal expansion of 2/sqrt(Pi).

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

Offset: 1

Author

Alonso del Arte, May 17 2011

Keywords

• nonn
• cons

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->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

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

Examples

			1.12837916709551257...
		

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
• Steven 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

Crossrefs

Cf. A002161, A019704, A285388, A285389.

Programs

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 *)

PARI

2/sqrt(Pi) \\ G. C. Greubel, Jan 09 2017

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