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I've looked over this Closed form formula for $\sum\limits_{k=1}^n k^k$ but it doesn't have any explicit formula, only the bounds.

So, is it the case that no general formula can exist to calculate it or we haven't found any formula yet?

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ankit
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  • This sequence grows quite rapidly - obviously larger than any particular degree of polynomial - the terms eventually exceed this degree. What makes you think a closed form exists then? It looks like any such formula would have to be exponential or larger. – A. Thomas Yerger Oct 05 '16 at 05:56
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    You should search the site before posting a duplicate:http://math.stackexchange.com/questions/45066/closed-form-formula-for-sum-limits-k-1n-kk – StubbornAtom Oct 05 '16 at 06:01
  • If you have looked over the other question then you should see that your actual question is also answered. – StubbornAtom Oct 05 '16 at 06:16
  • @StubbornAtom What do you mean? I've looked over the link and all it states is that there is no formula to calculate this but it doesn't answer is it the case that we can never have such formula or we haven't found yet but will be in the future. – ankit Oct 05 '16 at 06:23
  • You can very well understand that a closed-form formula hasn't been found, which is clear from the discussions there. It's the same query of the OP of that question too. – StubbornAtom Oct 05 '16 at 06:26
  • My question is would it be ever found or is it impossible to found?

    For example, uncertainity principle states that the position and velocity of a particle can't be measured simultaneously(below a certain level of certainity) and that is the property of the particle and not the limitation of humans.

     – ankit Oct 05 '16 at 06:30
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    Suppose that I was a famous mathematician and defined the polfosol's function as: $p(n)=\sum_{i=1}^n i^i$. Voila! here is the closed form – polfosol Oct 05 '16 at 06:58
  • It's not clear what you mean with "explicit" formula. What you can ask is e.g.: Can this sum expressed by a term build up by polynomials and the functions ... (you should complement this). :-) – user90369 Oct 05 '16 at 14:53

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