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Is there a theorem stating that all recursive problems cannot have a closed form? Or the other way around, stating that all recursive problems can have a closed form.

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closed as not a real question by William, tomasz, Chris Eagle, rschwieb, t.b. Sep 14 '12 at 17:48

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What definition of "closed form" are you using? –  J. M. Dec 30 '11 at 5:31
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I think what makes things hard to prove is the definition of "closed form". Very often, what we're calling "closed form" is just something satisfactory enough to work with, mostly written like "thing I want = weird but not too bad formula". –  Patrick Da Silva Dec 30 '11 at 5:57
    
@Sean, as written your question makes no sense. "recursive" has a very different meaning than the one I think you intended: If you were talking about recurrence relations you'll need to state that specifically. –  user16697 Dec 31 '11 at 7:18