# Change of bounds for Chebyshev polynomials

• Jun 14th 2011, 08:54 PM
n4538
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
• Jun 14th 2011, 10:23 PM
chisigma
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

$\displaystyle \chi$ $\displaystyle \sigma$
• Jun 14th 2011, 10:54 PM
theodds
Re: Change of bounds for Chebyshev polynomials
It's typical to use one of these guys: Sigmoid function - Wikipedia, the free encyclopedia
• Jun 22nd 2011, 03:12 PM
n4538
Re: Change of bounds for Chebyshev polynomials
Thank you both.