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Find a closed form for this sequence: $a_{n+1} = a_n + a_n^{-1}$
Suppose $$a_{n+1}=a_n+\frac{1}{a_n}$$ where $a_{1}=1$. Is $f(n)=a_n$ an elementary function?
I haven't found any paper concerning it. Thanks for your attention!
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1You might be interested in this paper. – J. M. ain't a mathematician Aug 20 '12 at 13:18
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1See also http://math.stackexchange.com/questions/63549/generating-functions-and-the-sequence-x-n1-x-n-frac1x-n – Antonio Vargas Aug 20 '12 at 13:20
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@J.M. Thanks a lot! – Golbez Aug 20 '12 at 13:24
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the elementariness remain unknown – Golbez Aug 20 '12 at 13:29
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1The paper proposed by @J.M. 'The Fractional Chromatic Number Of Mycielski's Graphs' is available at CiteSeer. – Raymond Manzoni Aug 20 '12 at 13:36
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References at http://oeis.org/A073833 – GEdgar Aug 20 '12 at 13:45
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I know some of the closed form such as $\sqrt{2n+\frac{\log{n}}{2}}$, but I need the elementariness of function $f$, not the upper/lower bound or equivalent infinite – Golbez Aug 20 '12 at 13:52