264 citations · 2.9k across the 87 of their papers we have counts for
87 papers
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…
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…
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…
Another Type of Forward and Backward Shift Relations for Orthogonal Polynomials in the Askey Scheme
Satoru Odake
The forward and backward shift relations are basic properties of the (basic) hypergeometric orthogonal polynomials in the Askey scheme (Jacobi, Askey-Wilson, -Racah, big -Jac…
New Finite Type Multi-Indexed Orthogonal Polynomials Obtained From State-Adding Darboux Transformations
Satoru Odake
The Hamiltonians of finite type discrete quantum mechanics with real shifts are real symmetric matrices of order . We discuss the Darboux transformations with higher degree ($…
"Diophantine'' and Factorisation Properties of Finite Orthogonal Polynomials in the Askey Scheme
Satoru Odake, Ryu Sasaki
A new interpretation and applications of the ``Diophantine'' and factorisation properties of {\em finite} orthogonal polynomials in the Askey scheme are explored. The corresponding…