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If we define $f(x)$ as some arbitrary function,

then we can define $f'(x)$ or $f^{(1)}(x)$ as the first order and $f''(x)$ or $f^{(2)}(x)$ as the second order.

My question is:

Is there sure thing as a $f^{(-1)}(x)$ notation? Could it be an antiderivative or an integration? And no, I am not talking about $f^{-1}(x)$ that represents an inverse of $f(x)$.

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    The notation is natural enough, though not at all common. I would be surprised if the usage is unprecedented. – John Coleman Jun 30 '16 at 16:57
  • I can't say that I have seen that notation before. Most common is to use capital letters to represent anti-derivatives and say something like F'(x) = f(x) – Doug M Jun 30 '16 at 17:37

1 Answers1

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I think a similar notation is used in the study of Fractional Calculus. The study of non integer integrals.

mathworld

I think this is the only field where the notation is used because its the only time I imagine needing a short hand for the 90th integral of something.

shai horowitz
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  • Probably the closest thing to what I'm talking about. Thanks for the answer! –  Jun 30 '16 at 18:40