You can create different types of footnote using the manyfoot package. If you want a special type of footnote to use in equations, then you can use two types and \ifmmode
to test whether you are currently in math mode. Personally, I would advise against using footnotes in equations, since the symbol or number can easily be mistaken for a piece of mathematical notation. Nevertheless...
\documentclass{article}
\usepackage{manyfoot}
\newcounter{footnoteA}
\newcommand\footnoteA{%
\stepcounter{footnoteA}%
\Footnotemark\thefootnoteA \FootnotetextA{}}
\newcounter{footnoteB}
\newcommand\footnoteB{%
\stepcounter{footnoteB}%
\Footnotemark\thefootnoteB \FootnotetextB\thefootnoteB}
\renewcommand{\thefootnoteB}{[\#\roman{footnoteB}]}
\newcommand\myfootnote[1]{\ifmmode\footnoteB{#1}\else\footnoteA{#1}\fi}
\newfootnote{A}
\newfootnote{B}
\usepackage{lipsum} %For dummy text
\begin{document}
\lipsum[1]\footnoteA{The quick brown fox jumps over the lazy dog}
\lipsum[2]\footnoteB{but lands on a sharp spike}
\lipsum[3]\myfootnote{and dies}
\[
e = mc^2\myfootnote{His advice from beyond is to avoid footnotes in equations.}
\]
\end{document}
The code for creating \footnoteA
and \footnoteB
is taken from the manyfoot package documentation.
\[…\]
instead of$$…$$