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Solve this with lower incomplete gamma function

  1. Oct 15, 2008 #1
    1. The problem statement, all variables and given/known data
    [tex]\int e^{-\frac{2Zr}{a}}*r^{-1}dr [/tex] Boundaries:[0,R]




    2. Relevant equations

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    3. The attempt at a solution
    I tried to solve this with lower incomplete gamma function and got [tex]\gamma[/tex](0,[tex]\frac{2ZR}{a}[/tex]) which is infinite i think.
    Z=81,a:Bohr radius,R=r0*A^(1/3) ,Th:A=203,r0=1,2*10^(-13)
     
  2. jcsd
  3. Oct 15, 2008 #2

    CompuChip

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    Re: Integral

    I don't know what the lower incomplete gamma function is, but Mathematica gives me
    [tex]\int_\epsilon^R \frac{1}{r} e^{-2Zr/a} \, \mathrm dr = \gamma(0, 2Z\epsilon/a) - \gamma(0, 2ZR/a)[/tex]
    which is finite for [itex]\epsilon > 0[/itex] but diverges for [itex]\epsilon \to 0[/itex].
     
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