I was thinking. I do not know whether my question has any sense.
- I want to know is there any way to compute analytically or explicitly some of the problems give below.
- What is the complexity of computing them?
- Is it worth to do it?
There are a lot of things that we know in mathematics especially in real analysis and we cannot compute explicitly such that:
1- Can anyone compute $\sum\limits_{n=1}^{N}\frac{1}{n^2}$ explicitly in function of $N$?
2- Can anyone find the integral of $e^{x^2}$, $\frac{1}{\text{log}x}$, $\dotsc$ explicitly?
There area a lot of other things that we all now.
Is it even necessary to compute them analytically? What is the real complexity of computing them?