HERMITE EQUATION AND POLYNOMIALS
HERMITE Equation is another special equation like LEGENDRE Differential Equation . It is used in the theory of linear harmonic oscillator in quantum mechanics . It is another special form of power series . The Differential Equation of the form y" - 2xy' + 2py = 0 ..........(1) where p is a constant , is called HERMITE DIFFERENTIAL EQUATION. Since -2x and 2p are analytic , x= 0 is an ordinary point of equation (1) and has a power series solution valid for all x . ∞ Let y = Σ cₙ xⁿ ........(2) n= 0 be a solution of equation (1) . Substituting for y, y' ,y" from equation (2) in equation (1) , we obtain ∞ ...