Looking for a way to insert formulas involving sums and integrals into a buffer

[Dan Hitt <dan.hitt@gmail.com>]

Using latex, you can easily write some random formula like
\[
    \int_a^b |f(t)|^2 dt = \sum_{j=0}^{\infty} \alpha_j^2
\]
After you convert the output dvi to pdf, it is easy to read.

I would like to do something like this in an emacs buffer that has loads of
other things in it, without much trouble.  Certainly i wouldn't want to
have to do anything multi-stage (like running latex, or compiling a file).

This would make it easier to keep notes, for example.

Now, what i can do is create an integral sign (using '\int' with tex input
mode in a text buffer), and create a capital sigma (\Sigma).  And there's
even limited creation of subscripts and superscripts, although lots of
symbols (such as \infty) cannot be turned into subscripts or superscripts.

On the other hand, i know that this sort of thing is possible in principle,
because if you look up, e.g., Parseval's identity in the wikipedia, it is
full of formulas.  If you copy/paste a wikipedia formula into an emacs
buffer, you get something that looks a lot like latex.  So somewhere along
the line something is doing something like latex-on-the-fly.

It would be nice, although i guess not required, if parts of formulas could
be colorized or bolded, as is possible in enriched mode.

The main requirement is that it be super-easy, without running additional
processes, and the result should be easily transportable (via copy/paste)
from buffer to buffer.

My version of emacs is 26.1, running on debian 10.

TIA for any info!

dan