A complicated taylor polynomial

1. Oct 11, 2007

IMDerek

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 $$e^{\cos x}$$. Thanks.

2. Oct 12, 2007

AiRAVATA

Well, for example, near [itex]\pi/2[/tex]

$$e^{\cos x}=1+\cos x+ \frac{cos^2 x}{2!}+\frac{\cos^3 x}{3!}+...$$

and

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

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
3. Oct 13, 2007

Gib Z

Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Similar Threads - complicated taylor polynomial Date
I Taylor expansion of f(x+a) Nov 1, 2017
Complicated Interpolation (Multivalued) Aug 14, 2012
Prove of the complicated integral Jan 16, 2012
Integral of complicated exponential functions Oct 30, 2011
Finding Complicated Inverse Functions Feb 15, 2011