Hi Ikumi,

I fixed the let/let* issues you noted.

> AUCTeX manual already has "Mathematics" node, so I think you should add
> explanation there.
> Examples are welcomed in the manual. Users who don't know elisp well
> will know how to use the prepaired function.

I've updated the attached patch with docs (so I think it's now in good
shape, but I always welcome feedback on my texinfo).

>> (defun my-LaTeX-make-brackets ()
>>   "Convert math construct at point to \"\\=\\[..\\=\\]\"."
>                                                   ^^^
> I'd suggest to remove quotation for \]. In contrast to \[, \] will be
> displayed literally without \=, though extra \= is harmless.

Done.  Any further feedback welcome!

Paul