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Help with serie summation

  1. Mar 5, 2008 #1
    Has anyone heard about a way to find the sum of a serie of this form:
    s=[tex]\sum_i{\exp(a+b\sqrt(i))}[/tex]
     
  2. jcsd
  3. Mar 5, 2008 #2

    tiny-tim

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    Hi yassermp! Welcome to PF! :smile:

    Why would you want to sum such a series? :confused:

    Have you noticed you can take the "a" outside the ∑, and write it:

    s = [tex]e^a\,\sum_n{e^{b\sqrt{n}}[/tex].
     
  4. Mar 6, 2008 #3
    Hi Tiny-tim

    Hi Tiny Tim, i see what you say, you are totally right. Essencially, that kind of sum arises when you try to sum contributions of several spherical waves, from scattering centers located at [tex]r_j=\sqrt{y^2+(z-z_j)^2}[/tex], with [tex]z_j=jh[/tex], j=1...n. The original sum is:
    s=[tex]\sum_j{e^{ikr_j}/r_j[/tex]
    Very often some approximations are used here, but i would like to obtain an exact analytical expression (no matter what complicated it could be). Id really thank any usefull sugestion(I know this is not an easy one). I tried a bit with some Fourier transform but i think it takes to an endless road.
    Thks
     
  5. Mar 6, 2008 #4

    tiny-tim

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    Hi yassermp!

    Sorry … but I can't help you there. :blushing:

    (btw, not a good idea to use i as an index when you're dealing with complex numbers! :smile:)
     
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