1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Trigonometric polynomial

  1. Dec 20, 2007 #1

    quasar987

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    1. The problem statement, all variables and given/known data
    Maybe I'm just blind, but how is

    [tex]T_n(x)=\left(\frac{1+\cos(t-a)}{b}\right)^n[/tex]

    of the form

    [tex]T_n(x)=\sum_{k=-n}^nc_ke^{ikx}[/tex]

    ???

    I can get

    [tex]\left(\frac{\cos(t-a)}{b}\right)^n[/tex]

    by setting

    [tex]c_{\pm n}=\left(\frac{e^{\mp ia}}{2b}\right)^n[/tex]

    and the rest of the c_k= 0, but how does the +1 comes in?
     
    Last edited: Dec 20, 2007
  2. jcsd
  3. Dec 20, 2007 #2

    HallsofIvy

    User Avatar
    Science Advisor

    ][tex](1+ a)^n= 1+ a+ _nC_2a^2+ ...+ a^{n-1}+ a^n[/itex] by the binomial theorem. Now use what you give to write each term as an exponential.
     
  4. Dec 20, 2007 #3

    quasar987

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    Ah!

    ----------
     
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook