Laguerre polynomials are 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 can be expressed using a specific formula involving factorials and powers. They are denoted as L_n(x) , where n is a non-negative integer. The first few Laguerre polynomials are simple to compute and serve as a basis for functions in quantum mechanics and other fields.