[math-fun] Analytic function with Fibonacci coefficients
8 Jan
2003
8 Jan
'03
3:51 p.m.
Just for fun, find f(z) = sum from k = 0 to oo of (F_n z^n), and its radius of convergence where F_n is the nth Fibonacci number (F_0 = 0, F_1 = 1,...). --Dan
9 Jan
9 Jan
1:45 p.m.
At 05:50 PM 1/8/03 -0500, asimovd@aol.com wrote:
Just for fun, find
f(z) = sum from k = 0 to oo of (F_n z^n),
and its radius of convergence
where F_n is the nth Fibonacci number (F_0 = 0, F_1 = 1,...).
This problem is exactly what turned me on to generating functions when I was in high school. Just a little more work yields the formula for F_n. -A
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Allan C. Wechsler -
asimovd＠aol.com