The function L_n(x) refers to the n -th Laguerre polynomial, which is a sequence of orthogonal polynomials used in various areas of mathematics and physics. These polynomials are defined on the interval [0, \infty) and are particularly useful in solving problems related to quantum mechanics, such as the radial part of the wave function for the hydrogen atom. Laguerre polynomials can be expressed using a specific formula involving factorials and powers of x . They are denoted as L_n(x) and satisfy a recurrence relation, making them easier to compute for higher values of n . Their orthogonality property ensures that they can be used effectively in approximation and numerical methods.