Hermite Polynomials are a set of orthogonal polynomials that arise in probability, combinatorics, and physics. They are defined using a specific recurrence relation and are often denoted as H_n(x), where n is a non-negative integer. These polynomials are particularly useful in solving problems related to the quantum harmonic oscillator in quantum mechanics. The properties of Hermite Polynomials include their orthogonality with respect to the weight function e^{-x^2} over the interval from negative to positive infinity. They also have applications in numerical analysis and approximation theory, making them valuable tools in various fields of science and engineering.