Chebyshev polynomials of the first kind

Site Home

Maths Home

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: 31 July 2021.

Thanks for visiting my site.