A086253 - OEIS

%I #28 Nov 26 2018 07:41:03

%S 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,

%T 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,

%U 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

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

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

%H G. C. Greubel, <a href="/A086253/b086253.txt">Table of n, a(n) for n = 1..10000</a>

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

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Feller%27s_coin-tossing_constants">Feller's coin-tossing constants</a>

%F Equals -2/3 - 4/(3*(17 + 3*sqrt(33))^(1/3)) +  2*(17 + 3*sqrt(33))^(1/3)/3. - _Vaclav Kotesovec_, Oct 14 2018

%F Positive real root of x^3 + 2*x^2 + 4*x - 8. - _Peter Luschny_, Oct 14 2018

%F Equals 2/A058265 = 2*A192918. - _Jon Maiga_, Nov 24 2018

%e 1.0873780253841527231417119436....

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

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

%o (PARI) solve(x=1, 3/2, 1-x+(x/2)^4) \\ _Michel Marcus_, Oct 14 2018

%Y Cf. A086254, A058265, A192918.

%K nonn,cons

%O 1,3

%A _Eric W. Weisstein_, Jul 13 2003