Chebyshev polynomials of the first kind

This site uses cookies & 3rd party adverts; click here for details. If you continue
to use this site I'll assume you're happy to accept this.
Site Home

Maths Home

Site Index

Calculator Index

About Us

Privacy Policy

Unfortunately, this page needs Java and your browser does not appear to support it.

Chebyshev polynomials, which are often written Tn(x), are a set orthogonal polynomials defined as the solutions to Chebyshev's differential equation


Chebyshev's differential equation

(1-x2)y''-xy'+n2y = 0

n = 0, 1, 2, ...

The first five Chebyshev polynomials are:


T0(x) = 1

T1(x) = x

T2(x) = 2x2 - 1

T3(x) = 4x3 - 3x

T4(x) = 8x4 - 8x2 + 1

These are plotted from -1 to +1 above.




Whilst I try to keep the information on this site accurate, I'm only human and I do occasionally make mistakes. I therefore advise you to check any information before using it for anything important. If you do find any errors, please let me know so that I can correct them.

Click here to report an error on this page.

This page was last changed on: 04 December 2017.

Thanks for visiting my site.