Confluence of apparent singularities in multi-indexed orthogonal polynomials : the Jacobi case
Confluence of apparent singularities in multi-indexed orthogonal polynomials : the Jacobi case
复制标题
多索引正交多项式中表观奇点的汇合：雅可比情况
DOI：
10.1088/1751-8113/46/11/115205
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发表时间：
2013
期刊：
影响因子：
--
通讯作者：
Kouichi TAKEMURA
中科院分区：
文献类型：
--
作者：
C.-L. Ho;Ryu Sasaki;Kouichi TAKEMURA
多指标Jacobi多项式是精确可解量子力学系统的特征函数的主要部分，该特征函数是通过Pöschl-Teller势的某些变形得到的。通过对Pöschl-Teller势的参数进行微调，我们得到了特征指数−2和−1具有明显奇点的二阶Fuchsian微分方程的若干显式和全局解族。它们在x∈(- 1,1)上形成正交多项式，其权函数的形式为(1 - x) α (1+ x) β/{(ax+ b) 4q (x) 2}，其中q (x)是x的多项式。
The multi-indexed Jacobi polynomials are the main part of the eigenfunctions of exactly solvable quantum mechanical systems obtained by certain deformations of the Pöschl–Teller potential (Odake–Sasaki). By fine-tuning the parameter (s) of the Pöschl–Teller potential, we obtain several families of explicit and global solutions of certain second-order Fuchsian differential equations with an apparent singularity of characteristic exponents− 2 and− 1. They form orthogonal polynomials over x∈(− 1, 1) with weight functions of the form (1− x) α (1+ x) β/{(ax+ b) 4 q (x) 2}, in which q (x) is a polynomial in x.