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A248751
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Decimal expansion of limit of the real part of f(1-i,n)/f(1-i,n+1), where f(x,n) is the n-th Fibonacci polynomial.
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3
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5, 2, 9, 0, 8, 5, 5, 1, 3, 6, 3, 5, 7, 4, 6, 1, 2, 5, 1, 6, 0, 9, 9, 0, 5, 2, 3, 7, 9, 0, 2, 2, 5, 2, 1, 0, 6, 1, 9, 3, 6, 5, 0, 4, 9, 8, 3, 8, 9, 0, 9, 7, 4, 3, 1, 4, 0, 7, 7, 1, 1, 7, 6, 3, 2, 0, 2, 3, 9, 8, 1, 1, 5, 7, 9, 1, 8, 9, 4, 6, 2, 7, 7, 1, 1, 4
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OFFSET
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0,1
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COMMENTS
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The analogous limit of f(1,n)/f(1,n+1) is the golden ratio (A001622).
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LINKS
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FORMULA
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EXAMPLE
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limit = 0.52908551363574612516099052379022521061936504...
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...
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MAPLE
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MATHEMATICA
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z = 300; t = Table[Fibonacci[n, x]/Fibonacci[n + 1, x], {n, 1, z}];
u = t /. x -> 1 - I;
d1 = N[Re[u][[z]], 130]
d2 = N[Im[u][[z]], 130]
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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