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Analytic Combinatorics – A Worked Example

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105 points mathgenius | 1 comments | 08 Apr 25 17:29 UTC | HN request time: 0.563s | source
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PollardsRho ◴[08 Apr 25 18:37 UTC] No.43625111[source]▶
Very cool!

What's meant by "it’s already too much to ask for a closed form for fibonacci numbers"? Binet's formula is usually called a closed form in my experience. Is "closed form" here supposed to mean "closed form we can evaluate without needing arbitrary-precision arithmetic"?

replies(3): >>43625353 #>>43626182 #>>43626796 #
1. paulpauper ◴[08 Apr 25 21:48 UTC] No.43626796[source]▶
It is closed form .the author makes so many mistakes here. All linear recusions are closed form by simply finding the roots of the characteristic equation. This is separate from the generating function, which the author confuses with the characteristic equation. A generating function is used when it's not possible to find a closed-form expression.