# Math Help - Change of bounds for Chebyshev polynomials

1. ## 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

2. ## Re: Change of bounds for Chebyshev polynomials

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

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

Kind regards

$\chi$ $\sigma$

3. ## Re: Change of bounds for Chebyshev polynomials

It's typical to use one of these guys: Sigmoid function - Wikipedia, the free encyclopedia

4. ## Re: Change of bounds for Chebyshev polynomials

Thank you both.