Multi-indexed Orthogonal Polynomials of a Discrete Variable and Exactly Solvable Birth and Death Processes

Satoru Odake

doi:10.1093/ptep/ptaf041

paper

Multi-indexed Orthogonal Polynomials of a Discrete Variable and Exactly Solvable Birth and Death Processes

arXiv:2501.02877 · doi:10.1093/ptep/ptaf041

Abstract

We present the case-(1) multi-indexed orthogonal polynomials of a discrete variable for 8 types ((dual)( $q$ -)Hahn, three kinds of $q$ -Krawtchouk and $q$ -Meixner). Based on them and the case-(1) multi-indexed orthogonal polynomials of Racah, $q$ -Racah, Meixner, little $q$ -Jacobi and little $q$ -Laguerre types, exactly solvable continuous time birth and death processes are obtained. Their discrete time versions (Markov chains) are also obtained for finite types.

35 pages. Typos are corrected. Comments and some data are added. To appear in PTEP