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An infinite sum

  1. Sep 28, 2014 #1

    tom.stoer

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    Does anybody know a closed for

    [tex]f(A,B) = \sum_{n\in\mathbb{Z}}e^{-Bn^2 + iAn}[/tex]

    with A real and B positive.
     
  2. jcsd
  3. Sep 28, 2014 #2

    mfb

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    Staff: Mentor

  4. Sep 28, 2014 #3

    tom.stoer

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    I can't believe that.
    I tried to calculate the density operator in position rep. for a particle on a circle. You get the exp(iAn) term from the eigenfunctions on the circle; A contains the angle. And you get the exp(-Bn2) from exp(-H/T).
    So it's nothing exotic.
     
  5. Sep 28, 2014 #4

    tom.stoer

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    Last edited: Sep 28, 2014
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