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What does closed form solution usually mean?
The Wikipedia article Closed-form expression states that such an expression can be defined "in terms of a bounded number of certain 'well-known' functions". I'm being confronted with an expression of the form $a_{n,k} = \sum_{i=0}^n(\mbox{closed-form expression in }i)$. Initially a recursive formula for the sequence $\{a_n\}$ of the form $a_n = (\mbox{closed-form expression in $a_n$})$ was given, so the sum is an explicit expression for the sequence. But would you also say, that it is a closed-form expression?
For every fixed $n$ it is a finite sum, so the number of certain "well-known" functions is bounded. But this is not valid for all $n$.
In this case, is the term closed-form expression clear without ambiguity? Could it be meant in both ways?
Edit: This might be confusing: of course for a fixed $n$ it's always easy to give a simple expression for $a_n$. For a fixed $n$ the expression for $a_n$ is just a number (even a natural number in my case). So the question is if the function $\sum$ is considered to be a "well-known" function. This might depend on the context, as answered here. Usually such a sum won't be considered as closed-form, because often we search for a closed-form expression for such a sum.
