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Meaning of complex term

  1. Jun 10, 2010 #1
    Hello
    In the following integral which I obtained from Wolfram, what is the physical meaning (e.g. in a heat conduction problem) of [tex]\sqrt{-\sinh^{2}(bx)}[/tex]. Also how to evaluate this at [tex]x=L[/tex].
    Thanks.

    [tex]
    \int\frac{dx}{\cosh^{3n+1}(bx)}=\frac{\sinh(bx)\cosh^{-3n}(bx)}{3nb\sqrt{-\sinh^{2}(bx)}}\,_{2}F_{1}\left(\frac{1}{2},-\frac{3n}{2};\frac{2-3n}{2};\cosh^{2}(bx)\right)
    [/tex]
     
  2. jcsd
  3. Jun 10, 2010 #2

    Gib Z

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    Homework Helper

    Welcome to PF!

    The antiderivative of a real function can not possibly be complex, So perhaps the hypergeometric function has imaginary terms that cancel it out.
     
    Last edited: Jun 10, 2010
  4. Jun 13, 2010 #3
    That is indeed the case as the parameters to the Hypergeometric function force it into it's analytic continuation giving rise to a imaginary number which cancels the i in the denominator.
     
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