Chebyshev function of the first kind

The Chebyshev polynomials of the first kind are a set of orthogonal polynomials defined as the solutions to the Chebyshev differential equation and denoted T_n(x). They are used as an approximation to a least squares fit, and are a special case of the Gegenbauer polynomial with α = 0. They are also intimately connected with trigonometric multiple-angle formulas. The Chebyshev polynomials of the first kind are denoted T_n(x), and are implemented in the Wolfram Language as ChebyshevT[n, x]. They are normalized such that T_n(1) = 1. The first few polynomials are illustrated above for x element [-1, 1] and n = 1, 2, ..., 5.

Chebyshev approximation formula | Chebyshev polynomial of the second kind