|
%I #8 Jul 13 2015 21:07:49
%S 2,0,5,8,2,9,5,6,0,8,2,3,5,1,7,3,9,1,0,6,7,8,6,5,2,3,9,5,8,9,8,6,4,5,
%T 1,8,6,8,8,4,1,7,1,9,5,4,9,4,0,7,8,9,4,9,6,1,1,4,7,8,9,6,0,6,1,0,5,2,
%U 4,6,3,6,6,0,5,5,4,5,1,6,2,1,4,7,7,4,1,3,5,0,9,2,1,4,1,8,5,0,0,5,7,4,9,5,4
%N Decimal expansion of the number c such that the solution to the differential functional equation f'(x) = f(x-1) + f(x-2) is c^x.
%C This is related to phi, as phi^x is the solution to f(x) = f(x-1) + f(x-2).
%F f(x-1) + f(x-2) = f'(x), f(x) = 2.058295608^x.
%p solve(ln(x)*x^2=x+1)
%p read("transforms3") ; Digits := 120 ; x := 2.0 ; for l from 1 to 10 do x := x-(x*log(x)-1-1/x)/(2*log(x)+1-1/x) ; x := evalf(x) ; end do; CONSTTOLIST(x) ; # _R. J. Mathar_, Mar 23 2010
%t digits = 105; c /. FindRoot[1 + 1/c == c*Log[c], {c, 2}, WorkingPrecision -> digits+5] // RealDigits[#, 10, digits]& // First (* _Jean-François Alcover_, Mar 05 2013 *)
%K cons,nonn
%O 1,1
%A Cameron Davidson-Pilon (see_dee_pee(AT)hotmail.com), Nov 26 2007
%E More digits from _R. J. Mathar_, Mar 23 2010
|
