New determinant expressions of multi-indexed orthogonal polynomials in discrete quantum mechanics

作者：Odake Satoru^*

来源：Progress of Theoretical and Experimental Physics, 2017, 2017(5): 053A01.

DOI：10.1093/ptep/ptx051

Multi-indexed orthogonal polynomials (the Meixner, little q-Jacobi (Laguerre), (q-) Racah, Wilson, and Askey-Wilson types) satisfying second-order difference equations were constructed in discrete quantum mechanics. They are polynomials in sinusoidal coordinates eta(x) (x is the coordinate of the quantum system) and are expressed in terms of Casorati determinants whose matrix elements are functions of x at various points. By using shape-invariance properties, we derive various equivalent determinant expressions, especially those whose matrix elements are functions of the same point x. Except for the (q-) Racah case, they can be expressed in terms of eta only, without explicit x-dependence.

• 出版日期2017-5