Change of bounds for Chebyshev polynomials

I need to change the region of a vector of observations from [-Inf:Inf] to [-1:1] to use with some higher order Chebyshev polynomials.

I know there is a tried and tested little function for doing this. Something like...1/1-exp(x^2.....).

I can't remember what this is. Would someone please be able to post this for me?

Many thanks,

J

Re: Change of bounds for Chebyshev polynomials

You have to find an odd function for which is $\displaystyle \lim_{x \rightarrow \infty} = 1$... a good candidate is...

$\displaystyle t= \frac{2}{\pi} \tan^{-1} x$

Kind regards

$\displaystyle \chi$ $\displaystyle \sigma$

Re: Change of bounds for Chebyshev polynomials

Re: Change of bounds for Chebyshev polynomials