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Solution to an exponential integral

  1. May 18, 2010 #1
    Hi,

    I am trying to find an analytic solution to the following double integral:

    [tex]
    \int_{0}^{2\pi}\int_{0}^{\pi}\sin\theta\exp\left(\frac{u^2}{a}\sin^{2}\theta+\frac{u^2}{b}\cos^{2}\theta-2u\left(\frac{v_x}{a}\sin\theta\cos\phi+\frac{v_y}{a}\sin\theta\sin\phi+\frac{v_z}{b}\cos\theta\right)\right)d\theta d\phi[/tex]

    I have tried using Mathematica and various substitutions but with no success. Using the result given in a previous post
    https://www.physicsforums.com/showthread.php?t=376233" , I know that in the limit of [tex]b=a[/tex] that the solution is


    [tex]
    \frac{2\pi\exp\left(\frac{u^2}{a}\right)}{\gamma}\left(\exp\left(\gamma\right)-\exp\left(-\gamma\right)\right)
    [/tex]

    where
    [tex]
    \gamma = \frac{2u}{a}\sqrt{v_x^2+v_y^2+v_z^2}\right)
    [/tex]

    but I cannot find the more general solution.
     
    Last edited by a moderator: Apr 25, 2017
  2. jcsd
  3. May 18, 2010 #2
    wont let you solve e^(sinx)
     
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