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Integration of mixed function at infinity limit

  1. Jun 28, 2013 #1
    Hi,

    I am trying to calculate second virial coefficient from interaction potentias and I have to Integrate at Infinity level and it seems that Integrate doesn't converge.

    can you help me integrate this function. Integrate is attached as an image.

    Regards
    Raymond
     

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  3. Jun 28, 2013 #2

    mathman

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    It looks like it would be difficult to integrate analytically. To check its behavior near r = 0, expand the numerator as a power series in r. The first term may be ~ r2, in which case you are OK. However I am not sure - it is messy.
     
  4. Jun 29, 2013 #3
    If rs is not nul, the integral is not convergent.
    So the integral can be computed only if rs=0
     
  5. Jun 29, 2013 #4

    mathman

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    Why???
     
  6. Jun 30, 2013 #5
    If rs is not nul, the function to be integrated is equivalent to c/r² close to r=0, where c is a constant (Expand the function around r=0).
    The integral of c/r² is divergent for r tending to 0.
    if rs=0 then c=0 and one can see from the expansion that the next term is integrable. So, there is no integration problem around r=0 in this particular case of rs=0.
    All this concerns the question of convergence around r=0 only.
     
    Last edited: Jun 30, 2013
  7. Jun 30, 2013 #6

    mathman

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    My estimate is that the numerator is ~ r2 near r = 0, unless s = 1.
     
  8. Jun 30, 2013 #7
    Does "rs" means r multiplied by s, or does "rs" is the symbol of a parameter (i.e. is constant) ?
    In the first case you are right. In the second case I am right.
     
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