I want to convert the first five terms of the Taylor series expansion for $e^x$ into Chebyshev Polynomial, but it requires that I express the power of $x$ as Chebyshev first, I've gotten it up to $x^3$. I got stuck after.
These are the first four... $x^0 =1$, $x=T_0(x)$, $x^2=T_1(x)$, $x^3=\frac{1}{4}(T_3(x)+3T_1(x))$, $x^4 =?$
Thanks in advance.