# Chebyshev polynomials

**Chebyshev polynomials** of the first kind are a set of orthogonal polynomials defined as the solutions to the Chebyshev differential equation and denoted
.
They are used as an approximation to a least squares fit,
and are a special case of the ultra-spherical polynomial (Gegenbauer polynomial)
with .
Chebyshev polynomial of the first kind, can be defined by the contour integral

The first seven Chebyshev polynomials of the first kind are:

## Orthogonality[edit]

The Chebyshev polynomials are orthogonal polynomials with respect to the weighting function such that

where is the Kronecker delta.