# Chebshev polynomial approximation

1. Oct 4, 2011

### sbashrawi

1. The problem statement, all variables and given/known data

Hi every body

I am triyng to find a polynolial approximation to the function: f(x)= (x+2)ln(x+2)
using the chebyshev polynomials,
the idea is to use matlab to find the coeefficients of the approximation poly.
using the comand double(int(...))
but this command doesn't give me any numerical value
Waht I got was:
>> int((x+2)*log(x+2)*(1-x^2)^-0.5,-1,1)
Warning: Explicit integral could not be found.
ans =
int((log(x + 2)*(x + 2))/(1 - x^2)^(1/2), x = -1..1)
>>
and if I use double(int(...)) an error message shows up
Any help pls

2. Relevant equations

3. The attempt at a solution

2. Oct 5, 2011

### TheoMcCloskey

Consider the substitution $x=\cos(\theta)$ and note that $T_k(x) = \cos(k \,\theta)$. This should remove the singularity.