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Math Help - Change of bounds for Chebyshev polynomials

  1. #1
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    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
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  2. #2
    MHF Contributor chisigma's Avatar
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    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
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  3. #3
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    Re: Change of bounds for Chebyshev polynomials

    It's typical to use one of these guys: Sigmoid function - Wikipedia, the free encyclopedia
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  4. #4
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    Re: Change of bounds for Chebyshev polynomials

    Thank you both.
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