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Integrate (ln ln x)^n

  1. Apr 16, 2009 #1
    How do you integrate (ln ln x)^n for any n?
     
  2. jcsd
  3. Apr 17, 2009 #2

    nicksauce

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    Well since mathematica isn't able to find a formula for n=2, I'm going to say "numerically".
     
  4. Apr 17, 2009 #3
    What do you mean exactly by "numerically"? Do you mean that i should evaluate it as a definite integral?
     
  5. Apr 17, 2009 #4

    nicksauce

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    Well I just mean if you want to find a general closed for expression for the indefinite integral, you are out of luck. Therefore the only way I can conceive of doing an integral with this expression would be to do a definite integral numerically.
     
  6. Apr 17, 2009 #5
    there is one place where the integral can be evaluated explicitly that I know of.
    [tex]\int[/tex]-log[-log[x]]dx=Euler Constant (.577...)
    This follows from differentionation the gamma function in its product and integral forms and making a change of variables.
     
  7. Apr 17, 2009 #6
    Although this method would be painful, since I cannot express this integral in terms of elementary functions, could I represent (ln ln x)^(n) as a Taylor polynomial (what is the Taylor series for ln ln x, anyways?) and then integrate that and leave it as a Taylor Series?
     
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