Hermite Polynomials Hermite polynomials is a polynomial that is defined by recurrence relation that: Hn(z)=2zHn−1(z)−2(n−1)Hn−2(z),H0(z)=1Explicitly, we have H0(z)=1H1(z)=2zH2(z)=4z2−2H3(z)=8z3−12zH4(z)=16z4−48z2+12⋮