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A086253
Decimal expansion of Feller's alpha coin-tossing constant.
3
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
1,3
REFERENCES
Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 5.11 Feller's coin tossing constants, p. 339.
LINKS
Eric Weisstein's World of Mathematics, Run
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
EXAMPLE
1.0873780253841527231417119436....
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 *)
PROG
(PARI) solve(x=1, 3/2, 1-x+(x/2)^4) \\ Michel Marcus, Oct 14 2018
CROSSREFS
KEYWORD
nonn,cons
AUTHOR
Eric W. Weisstein, Jul 13 2003
STATUS
approved