- #1
LS1088
- 3
- 1
Just curious. Is it possible to compute this? if yes then how?
I see three problems here:UltrafastPED said:Certainly ln(u) = x ln(x) would simplify things a bit ... your integrand is now e^u!
D H said:I see three problems here:
- That transformation is not a one-to-one onto mapping unless x is restricted to [1/e,∞).
- It might simplify the integrand, but it makes an absolute mess of dx.
That the transformation is not one-to-one onto makes it rather tough to deal with dx. Even if x is restricted to [1/e,∞), I get ##dx = du\,/\,(\operatorname W(\ln(u))+1)##, where W is the (non-elementary) Lambert W function.
- It still isn't integrable in the elementary functions.
Nope. x^x has a branch point at x=0. Your series is about x=0. It's radius of convergence is zero.jackmell said:Let's try anyway.
Well, we know:
[tex]e^u=\sum_{n=0}^{\infty} \frac{u^n}{n!}[/tex] then should not:
[tex]e^{x^x}=\sum_{n=0}^{\infty}\frac{(x^x)^n}{n!}=\sum_{n=0}^{\infty}\frac{x^{nx}}{n!}[/tex]
...
Won't that work?
D H said:Nope. x^x has a branch point at x=0. Your series is about x=0. It's radius of convergence is zero.
In[68]:=
NIntegrate[Exp[x^x], {x, 0.1, 2}]
NIntegrate[mye[x], {x, 0.1, 2}]
Out[68]=
13.451772502215917
Out[69]=
13.451772502215917
The concept of "Computing the Unsolvable" refers to the idea of finding a solution to a problem that is impossible to solve using traditional computing methods. This includes problems that are theoretically unsolvable, such as the halting problem, or problems that are computationally infeasible to solve, such as certain types of optimization or encryption problems.
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