Orthogonal polynomials are a set of polynomials that are mutually orthogonal with respect to a specific inner product. This means that the integral of the product of any two different polynomials in the set over a certain interval is zero. They are often used in various fields such as mathematics, physics, and engineering for solving problems involving approximation and numerical analysis. Common examples of orthogonal polynomials include Legendre polynomials, Chebyshev polynomials, and Hermite polynomials. These polynomials have important properties that make them useful for tasks like function approximation, spectral methods, and quantum mechanics. Their orthogonality simplifies calculations and helps in constructing efficient algorithms.