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Trigonometric integral - help needed

  1. Oct 7, 2006 #1
    need some assistance with the following integral:

    \int_0^{2\pi} cosx/(a-cosx), a-parameter (say a>0)

    i've converted it into a complex contour integral over z=e^(ix):

    ~ \int_{|z|=1} dz (z^2+1)/[z(z^2-2az+1)]

    which is easily evaluated for a>1. my question regards a<1 - i am not sure how to solve it in this case, because the the 2 poles

    z_1=a+Sqrt[a^2-1], z_2=a-Sqrt[a^2-1]

    are exactly on the unit circle and off the real axis. thanks for any suggestions!
     
  2. jcsd
  3. Oct 7, 2006 #2

    arildno

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    Hmm..is it really necessay to venture out in complexity here?
    Rational expressions in the trig. functions are easily handled by the transformation u=tan(x/2).
     
  4. Oct 7, 2006 #3
    it get's a bit complicated with this tan(x/2) substitution, with complex substitution it's very easily evaluated for a>1 and i'd like to find out what happens for a<1.
     
  5. Oct 7, 2006 #4

    arildno

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    Well, for a<1, the integral will readily diverge, so no wonder if you get into some problems.
     
  6. Oct 7, 2006 #5
    anyway, what is the principal value for a<1?
    thanks for your help, btw. i really appreciate it.
     
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