The function T_n(x) represents the Chebyshev polynomial of the first kind, which is a sequence of orthogonal polynomials. These polynomials are defined on the interval [-1, 1] and are particularly useful in approximation theory and numerical analysis. The n -th Chebyshev polynomial can be expressed using the cosine function: T_n(x) = \cos(n \cdot \arccos(x)) . Chebyshev polynomials have important properties, such as minimizing the maximum error in polynomial interpolation. They are widely used in various fields, including signal processing, computer graphics, and numerical methods, due to their ability to provide efficient approximations and their stability in computations.