论文标题
关于经典离散正交多项式的零的变化
On variation of zeros of classical discrete orthogonal polynomials
论文作者
论文摘要
本说明的目的是从Nikiforov和Uvarov引入的超几何型差方程来建立，这是针对经典离散正交多物质的真实参数的新型拖延的足够条件。该结果使人们可以对线性，二次，Q线性和Q-质量网格的经典正交多项式的零的单调性进行系统研究。特别是，我们以简单而统一的方式分析了Hahn，Charlier，Krawtchouk，Meixner，Racah，Dual Hahn，Q-Meixner，Quntum Q-Krawtchouk，Q-Krawtchouk，Affine q-Krawtchouk，Q-Krawtchouk，q-krawtchouk，q-krawtchouk，q-charlier，q-charlier，q-charlier，q-krah n salam-carlier， Q-JACOBI，LITTLE Q-LAGUERE/WALL，Q-BESSEL，Q-RACAH和双Q-HAHN多项式。
The purpose of this note is to establish, from the hypergeometric-type difference equation introduced by Nikiforov and Uvarov, new tractable sufficient conditions for the monotonicity with respect to a real parameter of zeros of classical discrete orthogonal polynomials. This result allows one to carry out a systematic study of the monotonicity of zeros of classical orthogonal polynomials on linear, quadratic, q-linear, and q-quadratic grids. In particular, we analyze in a simple and unified way the monotonicity of the zeros of Hahn, Charlier, Krawtchouk, Meixner, Racah, dual Hahn, q-Meixner, quantum q-Krawtchouk, q-Krawtchouk, affine q-Krawtchouk, q-Charlier, Al-Salam-Carlitz, q-Hahn, little q-Jacobi, little q-Laguerre/Wall, q-Bessel, q-Racah and dual q-Hahn polynomials.
