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Hadamard finite part integral

  1. Jun 7, 2009 #1
    Could someone provide a reference to calculate this kind of integrals ? for example

    [tex]\int_{0}^{2}dx \frac{cos(x)}{x-1} [/tex]

    or in 3-D [tex]\iiint_{D}dx \frac{x-y+z^{2})}{x+y+z} [/tex]

    Where 'D' is the cube [-1,1]x[-1,1]x[-1,1]=D

    as you can see there is a singularity at x=1 or whenever x+y+z=0 , perhaps the other integral is easier to define if we use polar coordinates , so the singularities appear when r=0
  2. jcsd
  3. Jun 7, 2009 #2


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    According to mathematica the integral does not converge.
  4. Jun 7, 2009 #3


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    Yes, ∫cosx/(x-1) dx near x = 1 is (cos1)∫dx/(x-1) = (cos1)[log(x-1)], which obviously is infinite. :smile:
  5. Jun 7, 2009 #4
  6. Jun 7, 2009 #5

    Gib Z

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  7. Jun 7, 2009 #6
    yes that is the definition , but in general you drop the divergent term dvided by epsilon and take only the finite value , that is for 1-D for 3-D or similar i do not know what can be done, or if the integral is divergent at infinity for example

    [tex] \int_{0}^{\infty}dxx^{3}cos(x) [/tex]
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