3 papers
math-ph2026
Some Difference Relations for Orthogonal Polynomials of a Continuous Variable in the Askey Scheme
Satoru Odake
Orthogonal polynomials of a continuous variable in the Askey scheme satisfying second order difference equations, such as the Askey-Wilson polynomial, can be studied by the quantum…
math-ph2025
Multi-indexed Orthogonal Polynomials of a Discrete Variable and Exactly Solvable Birth and Death Processes
Satoru Odake
We present the case-(1) multi-indexed orthogonal polynomials of a discrete variable for 8 types ((dual)(-)Hahn, three kinds of -Krawtchouk and -Meixner). Based on them and…
math-ph2025
Type II Multi-indexed Little -Jacobi and Little -Laguerre Polynomials
Satoru Odake
For the isospectral Darboux transformations of the discrete quantum mechanics with real shifts, there are two methods: type I and type II constructions. Based on the type I constru…