Math Formulas

If you mean searching for text with sub and super scripts, then yes, it's possible, but tricky. The idea is to acquire the median baseline and height of text on a line, then look for individual words that are smaller and above or below the baseline. If they exist, then you can extrapolate to find the complete formulas. But like I said, this is tricky and inexact stuff. You'd need a full blown AI to really do this correctly.

There are very few few formulas or functions stored within a PDF. Almost all are user written in JabaScript and aded by the author of the form. There some folder level functions to sum,  multiply, compute an average for some calcuation options. Exponentiation is done using JavaScript's Math.pow() or Math.exp() methods. JavaScript also supports array type variables.

For a detailed answer you might want to provide more specific details. Also Adobe has a number of tutorials and videos about creating forms and http://www.pdfscripting.com has a number of free examples as well as paid for examples and lessons.