Chebyshev polynomials are a sequence of orthogonal polynomials that play a central role in numerical analysis, approximation theory, and applied mathematics. They are named after the Russian mathematician Pafnuty Chebyshev and come in two primary types: Chebyshev polynomials of the first kind (\(T_n(x)\)) and Chebyshev polynomials of the second kind (\(U_n(x)\)). In this post we are going to focus on the Chebyshev polynomials of the first kind.