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

A complicated taylor polynomial

  1. Oct 11, 2007 #1
    Is there any nice trick for finding the Taylor polynomial of a composition of 2 functions, both of which can be expressed as taylor polynomials themselves? For example, finding the taylor polynomial for [tex]e^{\cos x}[/tex]. Thanks.
  2. jcsd
  3. Oct 12, 2007 #2
    Well, for example, near [itex]\pi/2[/tex]

    [tex]e^{\cos x}=1+\cos x+ \frac{cos^2 x}{2!}+\frac{\cos^3 x}{3!}+...[/tex]


    [tex]\cos x=-\frac{(x-\pi/2)^2}{2!}+\frac{(x-\pi/2)^4}{4!}-...[/tex]

    now, the hard part is to compose it, so maybe it's easier to just calculate the derivative and evaluate, depends on what are you looking for.
    Last edited: Oct 12, 2007
  4. Oct 13, 2007 #3

    Gib Z

    User Avatar
    Homework Helper

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