关于埃尔米特多项式的一些恒等式

Some Identities of the Hermite Polynomials

研究了埃尔米特多项式的一类和式的计算问题.利用埃尔米特多项式幂级数的生成函数及其可乘法则,通过对比两边幂级数的系数,以及对相关结论乘以系数后进行积分,得到关于埃尔米特多项式的一些恒等式.所得的恒等式简单而有趣,并有一定的推广性.

The main purpose of this paper is using Hermite polynomial generating functions,elementary methods and the nature of power series to study the calculating problem of one kind summation involving the Hermite polynomials and give some interesting identities.Orthogonal polynomials play a very important role in analysis and we also studied another important expansion contains Hermite polynomials.Using Hermite polynomial generating function and its multiplicative rule,by comparing both sides of the power series coefficients,reached a conclusion that proved Theorem 1.And also,multiplied by the coefficient on the relevant conclusions after integration,two specific theorems are derived.The identities are simple and interesting,and there are some promotional.