Asymptotic analysis of the Hermite polynomials from their differential–difference equation
Asymptotic analysis of the Hermite polynomials from their differential–difference equation
Abstract We analyze the Hermite polynomials H n (x) and their zeros asymptotically, as n → ∞ We obtain asymptotic approximations from the differential–difference equation which they satisfy, using the ray method. We give numerical examples showing the accuracy of our formulas. Keywords: Hermite polynomialsAsymptotic analysisRay methodOrthogonal polynomialsDifferential–difference equationsDiscrete WKB …