Hermite polynomials are a set of orthogonal polynomials that arise in probability, combinatorics, and physics. They are named after the French mathematician Charles Hermite and are defined using a specific recurrence relation. These polynomials are particularly important in quantum mechanics, where they appear in the solutions to the quantum harmonic oscillator problem. The general form of the Hermite polynomial is denoted as H_n(x), where n is a non-negative integer. Hermite polynomials can be expressed in terms of the exponential function and are used in various applications, including Gaussian integrals and statistical mechanics. Their orthogonality property makes them useful in approximating functions and solving differential equations.