关于正交多项式导数的正交性的注记

The Notes on Orthogonality of Derivatives of the Orthogonal Polynomial

首先讨论了Jacobi多项式的k阶导数在[-1,1]上关于权函数ρ(x)=(1-x)α+k(1+x)β+k是正交的,其结果比[2]更具有一般性,然后得到了Hermite多项式和Laguerre多项式的导数的正交性.

In this paper,the author firstly proves that k-order derivatives of Jacobi polynomial is an orthogonial system on the inverval with weight ρ(x)=(1-x)^(α+k)(1+x)^(β+k),and then obtains the orthogonlity of the k-order derivatives of Herimite polynomial and the k-order derivatives of Laguerre polynomial.