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

Complex Taylor series

  1. Mar 28, 2007 #1
    Assuming a complex function f(z) can be expanded as a Taylor series around z=0, i.e.:


    Setting z=r*exp(i*theta), assuming a_n is real, find real part u(r, theta), imaginary part v(r,theta).

    Comment the result, especially for r=1.

    [tex]f(z)=\sum_{n=0}^{\infty}a_{n}r^n(e^{i\theta})^n = \sum_{n=0}^{\infty}a_{n}r^n(cosn\theta+isinn\theta)[/tex]


    So I am to comment on the result.. What is there to say? I have "decomposed" the complex series into two real series, but this is kindo given; i'm sure they're asking for another comment.. Ideas?

    Is this an "optimal" solution BTW, or are there any other possibilities? Later on I'm asked to find real part of a expansion of ln.
  2. jcsd
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Can you offer guidance or do you also need help?