The Laguerre Polynomial is a sequence of orthogonal polynomials that arise in various areas of mathematics and physics, particularly in solving differential equations. They are defined on the interval from zero to infinity and are commonly used in quantum mechanics, especially in the context of the hydrogen atom. These polynomials are denoted as L_n(x), where n is a non-negative integer. The Laguerre Polynomials can be generated using a recurrence relation or through their explicit formula, which involves factorials. Their orthogonality property makes them useful in numerical analysis and approximation theory.