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:
The Chebyshev polynomials are orthogonal polynomials with respect to the weighting function such that
where is the Kronecker delta.