How to convert some LaTeX text to a high resolution PNG image

Create the TeX source file dump.tex like this:

\documentclass{article}
\pdfpagewidth2cm 
\pdfpageheight1cm
\hoffset-2.3cm
\voffset-2.3cm
\begin{document}
\shipout\hbox{$\infty \sum \int$}
\end{document}

Convert it to PDF:

% pdflatex dump.tex

Make sure that pk files don't appear on the console output of pdflatex. If they happen to appear, choose a different font, e.g. \usepackage{lmodern}.

Convert the PDF to PNG with Ghostscript:

% gs -dBATCH -dNOPAUSE -sDEVICE=pngmono -r1000 -sOutputFile=dump.png dump.pdf

If you need a larger resolution image, increase the number after the -r flag above.

This solution generates a PNG with sharp edges (no smoothing). If you take a screenshot of the PDF in a PDF viewer, or you load the PDF directly into GIMP, you'll most probably get a smoothed (antialiased) image.