Derivative and antiderivativeLet f be an infinitely differentiable real valued function. Can any condition be given under which n-th antiderivative of the n-th derivative of f is equal to f? Any help is appreciated.

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humusen6p · Accepted Answer

Step 1Let       f          (      n      )        =:  g. There is not &quot;the&quot;       n          t      h       antiderivative of g, but an n-dimensional affine space G of them. Two functions in G differ by a polynomial of degree   ≤  n  −  1, and exactly one element in G is   =  f.Step 2There are cases where f has a special property, e.g., being non-constant and bounded. In such a case it may happen that only one element of G has this property, and this element then has to be the f we started with.

Derivative and antiderivative Let f be an infinitely differentiable real valued

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