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Homework Help: Integration of a Derivative

  1. Jan 26, 2010 #1
    1. The problem statement, all variables and given/known data

    In general, what is [tex]\int_{0}^{\infty} f^{(n)}(z) dn[/tex]?

    2. Relevant equations



    3. The attempt at a solution
    Is the answer as simple as taking the antiderivative of n?
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Jan 28, 2010 #2
    n is the nth derivative of f(z), and z is a constant. I want to integrate with respect to the variable n, the nth derivative. If I simply took the aniderivative of n, and if the values I wanted to evaluate the integral over were 1 and 0, I would obtain [tex]f^{(1/2)}(z)[/tex] which does not make any sense. What am I doing wrong?
     
  4. Jan 28, 2010 #3

    Mark44

    Staff: Mentor

    The whole thing seems screwy to me. Your limits of integration are 0 to infinity, but derivatives make sense only for integer values of n. E.g., the "one-halfth" derivative doesn't make any sense.
     
  5. Jan 28, 2010 #4
    Does the integral even have an antiderivative, forgetting about the limits?
     
  6. Jan 28, 2010 #5
    This is the problem I am encountering in the Euler- MacLaurin expansion in my proof. The proof is given in another one of my posts called Zeta Function Proof. If anyone would like to point me in the right direction, I would appreciate it very much.
     
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