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Jacobi Eliiptic Theta Function

  1. Feb 25, 2008 #1

    I bother you again witha question concerning special functions.

    I have to evaluate


    From Mathworld ( http://mathworld.wolfram.com/InfiniteProduct.html formula 59) I know, that for x=1 this can be written as

    [tex]4^{\frac{1}{24}}\left(\theta_4\left[0,\frac{1}{4}\right]\right)^{-\frac{1}{2}}\left(\frac{1}{2} \theta_1'\left[0,\frac{1}{4}\right]\right)^{\frac{1}{6}}[/tex]

    where [tex]\theta_n\left[z,q\right][/tex] are the "famous" Elliptic Theta functions of Jacobi.

    Is there any chance to extend this to arbitrary real x?

    Mathworld and Abramowitz seem not to help me any further.


    A related representation ist the logarithmic derivative which I found to be


    Any ideas what function this might be ... for x=0 it's easy at least ..:smile:
    Last edited: Feb 25, 2008
  2. jcsd
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