Where can I find this? I'm a high school student learning outside the classroom, so I don't have access to any resources that require subscriptionThere *are* expressions for this. You might be able to find them in something like Boas or Arfken and Weber.
If you are familiar with differential forms, many (most? all?) proofs of the converse of Poincare's lemma also give the expressions that you want. See, e.g, Flanders.