Some Properties of Hermite Polynomials, their Squares and Cubes and Generating Functions

Abstract

In this thesis, the generating functions of the Hermite polyno mials, the squares of Hermite polynomials considered by (He & Yang, 2018) .We consider the generating functions of the Her mite polynomials and cubic Hermite polynomials. Pade approx- ´ imation used to solve the exponential function, present explicit formulas for higher order derivatives of the generating function. The Hermite polynomials and their cubic, which can be viewed as ordinary differential equations or derivative polynomials.The dif ferential equations that generating functions of the Hermite poly nomials and their cubic satisfied. Derive explicit formulas and recurrence relations for the Hermite polynomials and cubic Her mite polynom