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

Satoru Odake

doi:10.1093/ptep/ptaf041

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

Mathematical Physics 2026-04-02 v2 High Energy Physics - Theory Classical Analysis and ODEs math.MP Probability

Authors: Satoru Odake

View on arXiv ↗ PDF ↗ DOI ↗

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.

Keywords

multi-indexed orthogonal polynomials discrete variable birth and death processes Markov chains exactly solvable models

Cite

@article{arxiv.2501.02877,
  title  = {Multi-indexed Orthogonal Polynomials of a Discrete Variable and Exactly Solvable Birth and Death Processes},
  author = {Satoru Odake},
  journal= {arXiv preprint arXiv:2501.02877},
  year   = {2026}
}

Comments

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

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

Abstract

Keywords

Cite

Comments

Related papers