OFFSET
0,1
COMMENTS
The analogous limit of f(1,n)/f(1,n+1) is the golden ratio (A001622),
FORMULA
Equals (1-sqrt(sqrt(5)-2))/2. - Vaclav Kotesovec, Oct 19 2014
From Wolfdieter Lang, Mar 02 2018: (Start)
Equals (1 - (2 - phi)*sqrt(phi))/2, with phi = A001622.
Equals (1/10)*y*(1 - (1/50)*y^2) with y = A300070. (End)
EXAMPLE
limit = 0.2570658641216771609085680620527337189037570...
Let q(x,n) = f(x,n)/f(x,n+1) and c = 1-i.
n f(n,x) Re(q(c,n)) Im(q(c,n)))
1 1 1/2 1/2
2 x 3/5 1/5
3 1 + x^2 1/2 1/4
4 2x + x^3 8/15 4/15
5 1 + 3 x^2 + x^4 69/130 33/130
Re(q(11,1+i) = 5021/9490 = 0.5290832...
Im(q(11,1+i) = 4879/18980 = 0.275060...
MAPLE
evalf((1-sqrt(sqrt(5)-2))/2, 120); # Vaclav Kotesovec, Oct 19 2014
MATHEMATICA
CROSSREFS
KEYWORD
AUTHOR
Clark Kimberling, Oct 13 2014
STATUS
approved