Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

How to get the result?

  1. Jun 14, 2010 #1
    Example 1 in

    to get the Chebyshev expansion coefficient of ln(1 + x) is actually to calculate
    \int_{-\pi}^{\pi}\ln\left(1+\cos\theta \right)\cos\left(n\theta \right) d\theta
    where -\pi is the singluar point of the integration.
    Using complex analysis technique, it can be changed into
    \int \left[2\ln\left(1+z \right)-\ln z -\ln2 \right]\frac{z^n+z^\left(-n\
    where the integration path is the unit circle plus something else, since -1 is the branch point of ln(1 + z), just on the unit circle; 0 is the branch point of lnz and there should be a branch cut along the real axis and a infinitesmal small circle to get around the origin point. And I think the integration is divergent on this small circle.
    So I do not know how to get the result on that website.
    can anyone help?
  2. jcsd
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Can you offer guidance or do you also need help?
Draft saved Draft deleted