关于埃尔米特多项式卷积的正交性

On the orthogonality of the convolution of Hermite polynomials

关于正交多项式性质的研究是函数论及数论中的重要问题之一,本文研究了埃尔米特多项式Hn(x)的一类卷积的正交性.利用初等方法,结合正交多项式及幂级数的性质,得到了该类卷积定积分的一个精确的计算公式.

The properties of the orthogonal polynomial is one of the most important problems in function theory and number theory .In this paper ,the orthogonality of the kind of convolution of Hermite polyno‐mial Hn(x) was studied .By using elementary method and the properties of the power series ,an accurate calculation formula for the integral of the convolution was achieved .