Recently I posted a calculus problem Is there a closed form?.
In this problem, there is this dispute which interested me:
Here are the main points of the dispute which I want to talk about:
"For any value of , there is a solution set
And due to symmetry, is also a solution..."
This dispute impressed me as I did not manage to find the solutions for which
It happens that this does not include all the solutions and that for some values of , the solution for can be negative.
So, here is a challenge (which I can't solve):
Find the values of which has solutions for
Find a way to find the solutions of that are negative. (You can also try to find the complex solutions too, if there are)