Approach0
Searching for a specific formula is often rather difficult. A tool which is very suitable for this is the Approach0 search engine.
Some basic information can be found in Guide for New Users (which contains also animations of some examples). If you want to know more about the project, you can look at the documentation.
Approach0 uses mathquill editor and also offers a handy-pad for entering mathematical expressions. But for people familiar with $\rm\LaTeX$/MathJax it might be much easier to enter the expression directly in this form using raw query. (And you can also copy-paste a formula into this field from the source of some post on the site.)
The search results are presented with their title, a short preview of the contents, and (for search results from Mathematics SE) their tags. One can click on the title to open a posting in a separate tab. One can also click on a tag below a search result, that will restrict the result list to postings with that tag.
You can find some useful information also in the post by the creator of this program: Announcing a third-party search engine for Math StackExchange.
For example, this is what you get if you search for $\sum_{k=1}^n \frac1{k(k+1)}$. You can find many other examples of usage of this search engine if you look at comments and chat messages mentioning Approach0.
Although the "searching" chatroom has a more general purpose, quite a lot of the conversation in that room was devoted to Approach0.
Some stuff which is useful to keep in mind when using this search engine:
- Recent posts can be missing among the search results - depending on when the index was last updated.
- Approach0 is able - at least to some extent - to find posts where the same expression is written differently. (For example, names of a variables are changed, the sides of an equation are exchanged, etc.) But since this have some limits, you should try to think about various ways of writing the same expression. For example, when looking for posts about limit of Cesàro mean, you could try to search for $\lim_{n\to\infty}\frac{\sum_{k=1}^n a_k}n$,
or for $\lim_{n\to\infty} n^{-1}\sum_{k=1}^n a_k$,
or for $\lim_{n\to\infty}\frac1n\sum_{k=1}^n a_k)$,
or for $\lim_{n\to\infty}\frac{a_1+\dots+a_n}n$
Another example: You get different results if you search for $\lim_{x\to0}\frac{\sin(x)}x$ and if you search for $\lim_{x\to0}\frac{\sin x}x$.
- There is a distinction between
\infty and +\infty. For example, you get different results for $\lim_{x\to\infty} (1+\frac1n)^n$ and for $\lim_{x\to+\infty} (1+\frac1n)^n$ then the results are completely different.
- There is also a distinction between
|x| and \left|x\right|, Approach0 treats these two differently as a result of some technical considerations. For example, compare the search for $\frac{|x+y|}{1+|x+y|}\le\frac{|x|}{1+|x|}+\frac{|y|}{1+|y|}$ with and without including \left and \right.
- Check the parentheses! An extra or missing parenthesis might go unnoticed in a displayed formula, but makes a difference on Approach0: search for $\cos(x+y))$ vs search for $\cos(x+y)$.
Update: As of June 2021, Approach0 supports an extended query syntax. It allows to combine queries with logical operators, limit the results to certain sites (e.g. MSE), search in titles, tags, and so on.
Some examples (taken from here and here in the In the search of a question chat room):
Search for two formulas at the same time: OR content:$\cos x+\cos y+\cos z=1 $, AND content:$ \sin x+\sin y+\sin z=1$
Limit data source to MSE: OR content:$\sin\left(\omega t \right)$, AND site:math.stackexchange.com
\exact specifier for symbols: OR content:$\sin\left(\omega \exact t \right)$
Search for posts of some tags: OR content:$\sin\left(\omega t \right)$, AND tags:ordinary-differential-equations
Search keywords in only title field: OR content:$\sin\left(\omega t \right)$, AND title:solving
Use NOT clause to filter things: AND title:eigen, NOT title:vectors
