UPDATE DEC 2020
The equation editor was updated in Office 2018 onwards. Documentation for the new editor is here: https://support.microsoft.com/en-us/office/write-an-equation-or-formula-1d01cabc-ceb1-458d-bc70-7f9737722702
The functionality appears to largely be unaltered, so the information in this answer is likely to work, but I have not tested it. The white paper linked below is likely still relevant, though the original listing document has been removed and the link no longer works.
OLD ANSWER
A few months late, but I believe This is the document you are looking for. (LINK NOW DEAD) As best I can tell, OneNote 2013 uses the same equation editor as Word 2007/2010.
A whitepaper on the Word 2007 equation editor key commands can be found HERE on unicode.org.
TL;DR: Symbols are basically the same as in LaTeX, as are a few simple formatting commands like \thinsp, \sqrt, etc. From there, it is pretty good at figuring out what you mean if you type it the way you would try to type it in plaintext.
ALT+= enters an equation at the cursor point.
A handful of symbols:
\partial
\alpha \eta ο \omicron \upsilon
\beta \iota \pi \varpi
\chi \varphi \theta \omega
\delta \kappa \vartheta \xi
\epsilon \lambda \rho
Other handy notation:
\sum
\int
\scriptL
To add extra space:
\hairsp a small space
\thinsp a wider space
To add a function, type its name followed by a space:
sin<sp>\theta becomes sin
If a function is not recognized (like sinc), you can force apply function styling with \funcapply, by typing sinc\funcapply<sp>
Derivative ticks:
x′ x\prime<sp>
To do fractions, use /:
a/b
Parentheses are treated as a grouping character. For example, they would NOT show up in the fraction (a+b)/c. To get them to show, use ((a+b))/c. Delimiters (), [], and {} will automatically grow to the size of whatever is contained within them. You can pad the space within delimiters with \phantom and \vphantom.
The rest you will have to go read up on yourself, as Markdown doesn't support rendering LaTeX examples (AFAIK).
