Derivatives and Integrals are both what of a function?

Question

This is more a question on semantics. I'm writing a document and would like to describe a collection of functions that are both derivative and integral representations of a specific function. Is there any term or phrase to describe this group?

Answer 1

If you want to use a precise term that is not too common, various derivatives (first, second, etc.) and anti-derivatives could all be called "differintegrals" of the original function.

Depending on whether it is obvious to your audience from the context that anti-derivatives are to be included (they're almost like differentiating a negative number of times), I'd probably just accept the imprecision and use "derivatives" in your situation.

I can't think of anything else short for this, even the vague "results after applying operators" is too long.

Answer 2

Upto a constant the integral and differential coefficients of $ c e ^{\pm x} $ form the same set of functions.

Second differential order invariant function..