Laguerre Polynomials are a sequence of orthogonal polynomials that arise in various areas of mathematics and physics, particularly in quantum mechanics. They are defined on the interval from zero to infinity and are solutions to the Laguerre differential equation. These polynomials are commonly used in problems involving radial parts of wave functions in quantum systems. The general form of the n-th Laguerre polynomial is denoted as L_n(x). They have important properties, such as orthogonality with respect to the weight function e^{-x} on the interval [0, ∞). Laguerre polynomials also play a significant role in numerical analysis and approximation theory.