A086253 Decimal expansion of Feller's alpha coin-tossing constant.

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

Offset: 1

Author

Eric W. Weisstein, Jul 13 2003

Keywords

• nonn
• cons

Examples

			1.0873780253841527231417119436....
		

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. A086254, A058265, A192918.

Programs

Maple

evalf[120](solve(x^3+2*x^2+4*x-8=0,x)[1]); # Muniru A Asiru, Nov 25 2018

Mathematica

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

PARI

solve(x=1, 3/2, 1-x+(x/2)^4) \\ Michel Marcus, Oct 14 2018

Formula

Equals -2/3 - 4/(3*(17 + 3*sqrt(33))^(1/3)) + 2*(17 + 3*sqrt(33))^(1/3)/3. - Vaclav Kotesovec, Oct 14 2018

Positive real root of x^3 + 2*x^2 + 4*x - 8. - Peter Luschny, Oct 14 2018

Equals 2/A058265 = 2*A192918. - Jon Maiga, Nov 24 2018