$re = '/(\$`)(.*?)(`\$)/sm';
$str = 'p is prime. $`p_i`$ is the $`i^{th}`$ prime.
$`F(p)`$ is the set of factors `f` used to generate multiples of the prime `p`.
$`
\\begin{aligned}
\\dfrac{5}{2} r \\cdot \\dfrac{\\>\\>\\>\\frac{3}{2} w} {\\>1r}
&= \\frac{15}{4} w \\\\
&= \\>\\>3 \\frac{3}{4} \\>cups\\>water.
\\end{aligned}
`$
$`xyz`$
$``$
';
$subst = "\$$2\$";
$result = preg_replace($re, $subst, $str);
echo "The result of the substitution is ".$result;
Please keep in mind that these code samples are automatically generated and are not guaranteed to work. If you find any syntax errors, feel free to submit a bug report. For a full regex reference for PHP, please visit: http://php.net/manual/en/ref.pcre.php