A086254 Decimal expansion of Feller's beta coin-tossing constant.

1, 2, 3, 6, 8, 3, 9, 8, 4, 4, 6, 3, 8, 7, 8, 5, 1, 0, 1, 8, 9, 0, 6, 6, 0, 8, 7, 6, 1, 4, 2, 1, 2, 3, 2, 5, 2, 2, 1, 1, 1, 7, 6, 6, 2, 1, 2, 3, 5, 8, 8, 5, 8, 7, 3, 7, 1, 0, 7, 1, 6, 7, 2, 6, 7, 1, 5, 9, 0, 4, 2, 7, 4, 0, 0, 9, 2, 5, 8, 8, 1, 9, 1, 0, 7, 7, 8, 3, 8, 2, 6, 1, 3, 0, 6, 3, 9, 9, 3, 5, 7, 5, 9, 1

Offset: 1

Author

Eric W. Weisstein, Jul 13 2003

Keywords

• nonn
• cons

Examples

			1.2368398446387851018906608761421232....
		

References

• Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 5.11 Feller's coin tossing constants, p. 339.

Links

• G. C. Greubel, Table of n, a(n) for n = 1..10000
• Eric Weisstein's World of Mathematics, Run.
• Wikipedia, Feller's coin-tossing constants.

Crossrefs

Cf. A086253, A058265.

Programs

Magma

SetDefaultRealField(RealField(100)); (22 + (847 - 33*Sqrt(33))^(1/3) + (11*(77 + 3*Sqrt(33)))^(1/3))/33; // G. C. Greubel, Nov 25 2018

Maple

evalf[120](solve(11*x^3-22*x^2+12*x-2=0,x)[1]); # Muniru A Asiru, Nov 25 2018

Mathematica

alpha = Root[1-x+(x/2)^4, x, 1]; beta = (2-alpha)/(4-3*alpha); RealDigits[beta, 10, 102] // First (* Jean-François Alcover, Jun 03 2014 *)

PARI

default(realprecision, 100); (22 + (847 - 33*sqrt(33))^(1/3) + (11*(77 + 3*sqrt(33)))^(1/3))/33 \\ G. C. Greubel, Nov 25 2018

Sage

numerical_approx((22 + (847 - 33*sqrt(33))^(1/3) + (11*(77 + 3*sqrt(33)))^(1/3))/33, digits=100) # G. C. Greubel, Nov 25 2018

Formula

Equals (22 + (847 - 33*sqrt(33))^(1/3) + (11*(77 + 3*sqrt(33)))^(1/3))/33. - Vaclav Kotesovec, Oct 14 2018

Positive real root of 11*x^3 - 22*x^2 + 12*x - 2. - Peter Luschny, Oct 14 2018

Equals 2/(5 - A058265^2). - Jon Maiga, Nov 25 2018