On differential equations for orthogonal polynomials
On differential equations for orthogonal polynomials
复制标题
关于正交多项式的微分方程
DOI：
10.4310/maa.1998.v5.n4.a8
复制
发表时间：
1998
影响因子：
0.3
通讯作者：
J. Wimp
中科院分区：
文献类型：
--
作者：
M. Ismail;J. Wimp
我们找到了四阶微分方程解的四个线性独立解，这些解满足相应的雅可比多项式。证明了一般正交多项式的降阶算子中的系数满足非齐次四项递推关系，并进一步得到了它们的性质。此外，我们还证明了正整数c的伴随多项式{Pn(X)}满足一个四阶线性微分方程解的基，并对余递归多项式建立了类似的结果。
We find four linear independent solutions of the fourth-order differential equation satisfied by the associated Jacobi polynomials. We show that the coefficients in the lowering operator for general orthogonal polynomials satisfy inhomogeneous four-term recurrence relations and derive further properties of them. In addition, we show that the associated polynomials {Pn (x)} for positive integers c satisfy a linear differential equation of order four, we identify a basis of solutions of the differential equation, and we establish similar results for co-recursive polynomials.