# What happened to the interesting question about $L_1$ approximation of $x^n$?

Earlier this morning, there was an interesting question on this site about finding the closest approximation to $x^n$ by lower degree polynomials, in the $L^1$ norm on $[0,1]$.

I've figured out how to make Mathematica compute the answers almost immediately, and I'm seeing some interesting patterns in the answers, but I can't find the question anymore!

If the original user deleted this in response to the claim that this was in standard textbooks on approximation theory, then I will say that I don't think this is a good reason to delete it. I scanned through some online lecture notes on approximation theory before I started thinking about it, and I could only find the $L_2$ and $L_{\infty}$, not the $L_1$, cases. If experts know where to find this in textbooks, then let them post an explanation of this, but it isn't obvious to me.

• For 10k+ users: the question is here. I cast a vote to undelete the question because I am interested in seeing answers to this, too.
– t.b.
Jan 9, 2012 at 15:43
• A meta-comment: Moderators can search for deleted questions. However, this would work the best if you can provide some keywords in the original title of the question. I just tried searching for "approximate" and "approximation" and didn't find any that matched your description. It is a good thing that @t.b. remembered it, since questions deleted by the original owner are not listed in the 10K Tools. Jan 9, 2012 at 15:48
• The question is now undeleted.
– t.b.
Jan 9, 2012 at 16:44

## 1 Answer

For the sake of having an answer:

The post was deleted by the OP --- presumably in response to a comment suggesting that the result must be in any standard textbook on approximation theory. It is now undeleted by other users.

Let me add the following plea to all users asking questions in this site:

Please do not delete your post immediately if you find out that the answer can be found in Wikipedia/standard textbooks in a particular subject. Such a comment is not necessarily an implicit criticism of the question. Instead I imagine that the commenter only meant to help the OP find a more comprehensive reference for the problem. Thus rather than delete the thread, the OP could request for more focused pointers for references that address the specific question: this would benefit not only the OP but also the future visitors.

A similar remark also holds with regards to deleting a post that happens to be a duplicate of an earlier one.

• Hear hear. Sometimes the trick is to know which textbook contains the relevant result. That is one of the many ways Math.SE can be useful. Jan 10, 2012 at 14:54