What is the difference between closed-form expression and analytic expression?
I often see them get referenced in settings where (in my opinion) they are essentially interchangeable.
What is a tangible difference between them, such as something one can do whereas the other cannot?
$\endgroup$ 12 Answers
$\begingroup$We wouldn't say "closed-form" for the solution of a differential equation, neither "analytic expression" for the solution of a difference equation (at least this is my impression). On the other hand, most probably, in this particular example we would use them interchanged!
But yes, I would say that they are essentially interchangeable. I would use also "explicit form" (again essentially interchangeable with those that you mention).
$\endgroup$ 3 $\begingroup$I also think they are synonyms.
$\endgroup$A solution to a problem that can be written in "closed form" in terms of known functions, constants, etc., is often called an analytic solution.
